SSL inverse.tst
Interaktion und
Portierbarkeitunbekannt
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Spracherkennung für: .tst vermutete Sprache: Unknown {[0] [0] [0]} [Methode: Schwerpunktbildung, einfache Gewichte, sechs Dimensionen]
#############################################################################
##
#W standard/attributes/inverse.tst
#Y Copyright (C) 2015- 2022 Wilf A. Wilson
##
## Licensing information can be found in the README file of this package.
#
#############################################################################
##
#@local D, I, S, T, W, acting, an, elts, es, f, foo, gens, h, iso, jid, n, reps
#@local small, x
gap> START_TEST("Semigroups package: standard/attributes/inverse.tst");
gap> LoadPackage("semigroups", false);;
#
gap> SEMIGROUPS.StartTest();
# attrinv: VagnerPrestonRepresentation, symmetric inv monoid 4 1/ 1
gap> S := InverseSemigroup([
> PartialPerm([ 2, 3, 4, 1]),
> PartialPerm([ 2, 1, 3, 4]),
> PartialPerm([ 1, 2, 3, 0])]);;
gap> Size(S);
209
gap> Size(S) = Size(SymmetricInverseMonoid( 4));
true
gap> iso := VagnerPrestonRepresentation(S);;
gap> DegreeOfPartialPermSemigroup(Range(iso));
209
# attrinv: SameMinorantsSubgroup, symmetric inv monoid 5 1/ 2
gap> S := SymmetricInverseSemigroup( 5);;
gap> h := HClass(S, One(S));
<Green's H-class: <identity partial perm on [ 1, 2, 3, 4, 5 ]>>
gap> SameMinorantsSubgroup(h);
[ <identity partial perm on [ 1, 2, 3, 4, 5 ]> ]
gap> h := HClass(S, PartialPerm([ 1, 2, 0, 0, 0]));
<Green's H-class: <identity partial perm on [ 1, 2 ]>>
gap> SameMinorantsSubgroup(h);
[ <identity partial perm on [ 1, 2 ]> ]
gap> h := HClass(S, MultiplicativeZero(S));
<Green's H-class: <empty partial perm>>
gap> SameMinorantsSubgroup(h);
[ <empty partial perm> ]
# attrinv: SameMinorantsSubgroup, error 2/ 2
gap> S := FullTransformationMonoid( 5);;
gap> h := HClass(S, One(S));
<Green's H-class: IdentityTransformation>
gap> SameMinorantsSubgroup(h);
Error, the parent of the argument (a group H-class) must be an inverse semigro\
up
# attrinv: Minorants, error, 1
gap> S := SymmetricInverseMonoid( 3);;
gap> f := PartialPerm([ 1, 2, 3, 4]);;
gap> Minorants(S, f);
Error, the 2nd argument (a mult. elt.) is not an element of the 1st argument (\
an inverse semigroup)
gap> f := PartialPerm([ 1, 2, 3]);;
gap> Set(Minorants(S, f));
[ <empty partial perm>, <identity partial perm on [ 1 ]>,
<identity partial perm on [ 2 ]>, <identity partial perm on [ 1, 2 ]>,
<identity partial perm on [ 3 ]>, <identity partial perm on [ 2, 3 ]>,
<identity partial perm on [ 1, 3 ]> ]
gap> NaturalPartialOrder(S);;
gap> Minorants(S, f);
[ <empty partial perm>, <identity partial perm on [ 1 ]>,
<identity partial perm on [ 2 ]>, <identity partial perm on [ 1, 2 ]>,
<identity partial perm on [ 3 ]>, <identity partial perm on [ 2, 3 ]>,
<identity partial perm on [ 1, 3 ]> ]
gap> f := PartialPerm([ 1, 3, 2]);;
# attrinv: Minorants, not idempotent, 2
gap> S := Semigroup([
> PartialPerm([ 1, 2, 3, 4], [ 1, 2, 3, 4]),
> PartialPerm([ 1, 2, 3], [ 2, 3, 1])]);;
gap> IsInverseSemigroup(S);
true
gap> Minorants(S, GeneratorsOfSemigroup(S)[ 2]);
[ ]
gap> S := Semigroup(S, rec(acting := false));;
gap> IsInverseSemigroup(S);
true
gap> Minorants(S, GeneratorsOfSemigroup(S)[ 1]);
[ <identity partial perm on [ 1, 2, 3 ]> ]
# attrinv: character tables of inverse acting semigroups
# Some random examples to test consistency of old code with new
gap> gens := [
> [PartialPerm([ 1, 2, 3, 4, 6, 8, 9], [ 1, 5, 3, 8, 9, 4, 10])],
> [PartialPerm([ 1, 2, 3, 4, 5, 6], [ 3, 8, 4, 6, 5, 7]),
> PartialPerm([ 1, 2, 3, 4, 5, 7], [ 1, 4, 3, 2, 7, 6]),
> PartialPerm([ 1, 2, 3, 5, 6, 8], [ 5, 7, 1, 4, 2, 6])],
> [PartialPerm([ 1, 2, 3, 5], [ 2, 1, 7, 3]),
> PartialPerm([ 1, 2, 4, 5, 6], [ 7, 3, 1, 4, 2]),
> PartialPerm([ 1, 2, 3, 4, 6], [ 7, 6, 5, 1, 2]),
> PartialPerm([ 1, 3, 6, 7], [ 6, 3, 1, 4])],
> [PartialPerm([ 1, 2, 3, 5], [ 1, 6, 4, 7]),
> PartialPerm([ 1, 2, 3, 6], [ 1, 6, 5, 2]),
> PartialPerm([ 1, 2, 3, 5, 6, 7], [ 4, 3, 5, 7, 1, 6]),
> PartialPerm([ 1, 2, 3, 4, 7], [ 6, 4, 2, 3, 1])],
> [PartialPerm([ 1, 2, 3, 5, 6], [ 5, 3, 7, 4, 1]),
> PartialPerm([ 1, 2, 3, 4, 5, 7], [ 3, 1, 5, 7, 6, 2])],
> [PartialPerm([ 1, 2, 3, 4, 5, 6, 9], [ 1, 5, 9, 2, 6, 10, 7]),
> PartialPerm([ 1, 3, 4, 7, 8, 9], [ 9, 4, 1, 6, 2, 8]),
> PartialPerm([ 1, 2, 3, 4, 5, 9], [ 9, 3, 8, 2, 10, 7])],
> [PartialPerm([ 1, 2, 3, 4, 5], [ 6, 4, 1, 2, 7]),
> PartialPerm([ 1, 2, 3, 6], [ 3, 5, 7, 4]),
> PartialPerm([ 1, 2, 3, 4, 5, 6, 7], [ 1, 7, 9, 5, 2, 8, 4])],
> [PartialPerm([ 1, 2, 4], [ 3, 6, 2]),
> PartialPerm([ 1, 2, 3, 4], [ 6, 3, 2, 1]),
> PartialPerm([ 1, 2, 3, 6], [ 4, 6, 3, 1]),
> PartialPerm([ 1, 2, 3, 5, 6], [ 5, 6, 3, 2, 4])],
> [PartialPerm([ 1, 2, 3, 4], [ 3, 5, 1, 2]),
> PartialPerm([ 1, 2, 3, 4], [ 5, 4, 2, 1]),
> PartialPerm([ 1, 2, 4, 5], [ 3, 5, 1, 2])],
> [PartialPerm([ 1, 2, 3, 5], [ 4, 1, 2, 3])]];;
gap> S := List(gens, x -> InverseSemigroup(x, rec(acting := true)));
[ <inverse partial perm semigroup of rank 9 with 1 generator>,
<inverse partial perm semigroup of rank 8 with 3 generators>,
<inverse partial perm semigroup of rank 7 with 4 generators>,
<inverse partial perm semigroup of rank 7 with 4 generators>,
<inverse partial perm semigroup of rank 7 with 2 generators>,
<inverse partial perm semigroup of rank 10 with 3 generators>,
<inverse partial perm semigroup of rank 9 with 3 generators>,
<inverse partial perm semigroup of rank 6 with 4 generators>,
<inverse partial perm semigroup of rank 5 with 3 generators>,
<inverse partial perm semigroup of rank 5 with 1 generator> ]
#@if CompareVersionNumbers(ReplacedString(GAPInfo.Version, "dev", ""), " 4. 15")
gap> CharacterTableOfInverseSemigroup(S[ 1]);
[ [ [ 1, 0, 0, 0 ], [ 2, 1, 0, 0 ], [ 1, 1, 1, - 1 ], [ 1, 1, 1, 1 ] ],
[ <identity partial perm on [ 1, 3, 4, 5, 8, 9, 10 ]>,
<identity partial perm on [ 1, 3, 4, 6, 8 ]>,
<identity partial perm on [ 1, 3, 4, 8 ]>, ( 1)( 3)( 4, 8) ] ]
gap> CharacterTableOfInverseSemigroup(S[ 2]);
[ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 3, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 4, 4, 0, 1, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 3, 3, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 4, 3, 3, 2, 1, 2, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 4, 3, 3, 2, 1, 2, 0, 0, 0, 1, E( 3), E( 3)^ 2, 0, 0, 0, 0, 0, 0, 0, 0, 0
], [ 4, 3, 3, 2, 1, 2, 0, 0, 0, 1, E( 3)^ 2, E( 3), 0, 0, 0, 0, 0, 0,
0, 0, 0 ],
[ 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, - 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 19, 19, 20, 10, 9, 10, 4, 4, 4, 4, 1, 1, 3, - 1, 1, - 1, 1, 0, 0, 0, 0 ]
, [ 38, 38, 40, 20, 18, 20, 8, 8, 8, 8, - 1, - 1, 6, 0, 2, 0, - 1, 0, 0,
0, 0 ],
[ 19, 19, 20, 10, 9, 10, 4, 4, 4, 4, 1, 1, 3, 1, 1, 1, 1, 0, 0, 0, 0 ],
[ 15, 15, 15, 10, 10, 10, 6, 6, 6, 6, 0, 0, 6, 0, 3, - 1, 0, 1, - 1, 0, 0
], [ 15, 15, 15, 10, 10, 10, 6, 6, 6, 6, 0, 0, 6, 2, 3, 1, 0, 1, 1,
0, 0 ],
[ 6, 6, 6, 5, 5, 5, 4, 4, 4, 4, 1, 1, 4, 2, 3, 1, 0, 2, 0, 1, 0 ],
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ] ],
[ <identity partial perm on [ 3, 4, 5, 6, 7, 8 ]>,
<identity partial perm on [ 1, 2, 3, 4, 6, 7 ]>,
<identity partial perm on [ 1, 2, 4, 5, 6, 7 ]>,
<identity partial perm on [ 1, 3, 5, 6, 8 ]>,
<identity partial perm on [ 1, 2, 3, 4, 7 ]>,
<identity partial perm on [ 1, 2, 4, 5, 7 ]>,
<identity partial perm on [ 1, 3, 6, 8 ]>,
<identity partial perm on [ 1, 3, 4, 7 ]>,
<identity partial perm on [ 2, 3, 5, 7 ]>,
<identity partial perm on [ 1, 2, 4, 6 ]>, ( 1)( 2, 4, 6), ( 1)( 2, 6, 4),
<identity partial perm on [ 1, 2, 3, 4 ]>, ( 1)( 2, 4)( 3),
<identity partial perm on [ 2, 5, 7 ]>, ( 2)( 5, 7), ( 2, 5, 7),
<identity partial perm on [ 2, 5 ]>, ( 2, 5),
<identity partial perm on [ 6 ]>, <empty partial perm> ] ]
gap> CharacterTableOfInverseSemigroup(S[ 3]);
[ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 6, 6, 4, 2, 2, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 1, 0, 0, 0, 0, 1, - 1, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0 ],
[ 2, 2, 0, 0, 1, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 10, 10, 6, 6, 6, 6, 3, 3, 3, - 1, 3, 1, - 1, 0, 0 ],
[ 10, 10, 6, 6, 6, 6, 3, 3, 3, 1, 3, 1, 1, 0, 0 ],
[ 5, 5, 4, 4, 4, 4, 3, 3, 3, 1, 3, 2, 0, 1, 0 ],
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ] ],
[ <identity partial perm on [ 1, 2, 3, 4, 7 ]>,
<identity partial perm on [ 1, 2, 5, 6, 7 ]>,
<identity partial perm on [ 1, 2, 3, 7 ]>,
<identity partial perm on [ 1, 3, 6, 7 ]>,
<identity partial perm on [ 1, 5, 6, 7 ]>,
<identity partial perm on [ 2, 3, 4, 6 ]>,
<identity partial perm on [ 3, 6, 7 ]>,
<identity partial perm on [ 5, 6, 7 ]>,
<identity partial perm on [ 1, 3, 6 ]>, ( 1, 6)( 3),
<identity partial perm on [ 1, 5, 6 ]>,
<identity partial perm on [ 3, 7 ]>, ( 3, 7),
<identity partial perm on [ 1 ]>, <empty partial perm> ] ]
gap> CharacterTableOfInverseSemigroup(S[ 4]);
[ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 4, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 0, 1, 0, 0, 0, 0, 1, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 20, 10, 9, 4, 4, 3, 4, 4, 0, 1, - 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 20, 10, 9, 4, 4, 3, 4, 4, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, E( 3), E( 3)^ 2, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, E( 3)^ 2, E( 3), 0, 0, 0, 0 ],
[ 15, 10, 10, 6, 6, 6, 6, 6, - 2, 3, - 1, 3, 0, 0, 1, - 1, 0, 0 ],
[ 15, 10, 10, 6, 6, 6, 6, 6, 2, 3, 1, 3, 0, 0, 1, 1, 0, 0 ],
[ 6, 5, 5, 4, 4, 4, 4, 4, 0, 3, 1, 3, 0, 0, 2, 0, 1, 0 ],
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ] ],
[ <identity partial perm on [ 1, 3, 4, 5, 6, 7 ]>,
<identity partial perm on [ 2, 3, 5, 6, 7 ]>,
<identity partial perm on [ 1, 2, 3, 4, 6 ]>,
<identity partial perm on [ 1, 2, 4, 7 ]>,
<identity partial perm on [ 1, 4, 6, 7 ]>,
<identity partial perm on [ 2, 3, 4, 7 ]>,
<identity partial perm on [ 1, 2, 4, 6 ]>,
<identity partial perm on [ 1, 2, 5, 6 ]>, ( 1, 5)( 2, 6),
<identity partial perm on [ 1, 3, 6 ]>, ( 1)( 3, 6),
<identity partial perm on [ 2, 3, 4 ]>, ( 2, 3, 4), ( 2, 4, 3),
<identity partial perm on [ 1, 2 ]>, ( 1, 2),
<identity partial perm on [ 1 ]>, <empty partial perm> ] ]
gap> CharacterTableOfInverseSemigroup(S[ 5]);
[ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 3, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 7, 3, 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 5, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0 ]
, [ 19, 10, 4, 4, 1, 1, 1, 0, 0, 0, 0 ],
[ 19, 10, 4, 4, 1, E( 3), E( 3)^ 2, 0, 0, 0, 0 ],
[ 19, 10, 4, 4, 1, E( 3)^ 2, E( 3), 0, 0, 0, 0 ],
[ 15, 10, 6, 6, 3, 0, 0, 1, - 1, 0, 0 ],
[ 15, 10, 6, 6, 3, 0, 0, 1, 1, 0, 0 ],
[ 6, 5, 4, 4, 3, 0, 0, 2, 0, 1, 0 ],
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ] ],
[ <identity partial perm on [ 1, 2, 3, 5, 6, 7 ]>,
<identity partial perm on [ 1, 3, 4, 5, 7 ]>,
<identity partial perm on [ 1, 2, 3, 6 ]>,
<identity partial perm on [ 1, 3, 5, 6 ]>,
<identity partial perm on [ 1, 2, 6 ]>, ( 1, 2, 6), ( 1, 6, 2),
<identity partial perm on [ 1, 3 ]>, ( 1, 3),
<identity partial perm on [ 4 ]>, <empty partial perm> ] ]
gap> CharacterTableOfInverseSemigroup(S[ 6]);
[ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 2, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 3, 2, 1, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 4, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 3, 1, 1, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 5, 3, 2, 2, 2, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 4, 4, 6, 1, 2, 1, 3, 1, 2, 1, 1, 0, 0, 0, 0, 0, 1, - 1, 1, 0, 0, 0, 0 ]
, [ 8, 8, 12, 2, 4, 2, 6, 2, 4, 2, 2, 0, 0, 0, 0, 0, 2, 0, - 1, 0, 0,
0, 0 ],
[ 4, 4, 6, 1, 2, 1, 3, 1, 2, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0 ],
[ 21, 15, 15, 10, 10, 6, 6, 6, 6, 6, 6, 3, 3, 3, 3, 3, 3, - 1, 0, 1, - 1,
0, 0 ],
[ 21, 15, 15, 10, 10, 6, 6, 6, 6, 6, 6, 3, 3, 3, 3, 3, 3, 1, 0, 1, 1,
0, 0 ],
[ 7, 6, 6, 5, 5, 4, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 1, 0, 2, 0, 1, 0 ],
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ]
],
[ <identity partial perm on [ 1, 2, 5, 6, 7, 9, 10 ]>,
<identity partial perm on [ 2, 3, 7, 8, 9, 10 ]>,
<identity partial perm on [ 1, 2, 4, 6, 8, 9 ]>,
<identity partial perm on [ 1, 5, 6, 7, 10 ]>,
<identity partial perm on [ 1, 3, 4, 7, 8 ]>,
<identity partial perm on [ 3, 7, 9, 10 ]>,
<identity partial perm on [ 1, 4, 8, 9 ]>,
<identity partial perm on [ 3, 4, 6, 9 ]>,
<identity partial perm on [ 1, 3, 4, 8 ]>,
<identity partial perm on [ 1, 4, 7, 8 ]>,
<identity partial perm on [ 2, 4, 6, 8 ]>,
<identity partial perm on [ 3, 6, 9 ]>,
<identity partial perm on [ 6, 8, 9 ]>,
<identity partial perm on [ 1, 3, 7 ]>,
<identity partial perm on [ 3, 4, 6 ]>,
<identity partial perm on [ 1, 2, 4 ]>,
<identity partial perm on [ 1, 3, 4 ]>, ( 1)( 3, 4), ( 1, 3, 4),
<identity partial perm on [ 1, 3 ]>, ( 1, 3),
<identity partial perm on [ 1 ]>, <empty partial perm> ] ]
gap> CharacterTableOfInverseSemigroup(S[ 7]);
[ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 1, - 1, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, - 1, -E( 4), E( 4), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, - 1, E( 4), -E( 4), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 6, 4, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 5, 4, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 3, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 4, 2, - 2, 0, 0, 2, 1, 0, 0, 0, 1, - 1, 0, 0, 0, 0, 0 ],
[ 4, 2, 2, 0, 0, 2, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0 ],
[ 10, 4, 0, 0, 0, 5, 2, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 20, 10, - 2, 0, 0, 10, 6, 6, 3, 3, 3, - 1, 3, 1, - 1, 0, 0 ],
[ 20, 10, 2, 0, 0, 10, 6, 6, 3, 3, 3, 1, 3, 1, 1, 0, 0 ],
[ 7, 5, 1, 1, 1, 5, 4, 4, 3, 3, 3, 1, 3, 2, 0, 1, 0 ],
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ] ],
[ <identity partial perm on [ 1, 2, 4, 5, 7, 8, 9 ]>,
<identity partial perm on [ 1, 2, 4, 5, 7 ]>, ( 1)( 2, 4)( 5, 7),
( 1)( 2, 5, 4, 7), ( 1)( 2, 7, 4, 5), <identity partial perm on [ 1, 2, 4, 6, 7 ]>
, <identity partial perm on [ 1, 2, 4, 7 ]>,
<identity partial perm on [ 3, 4, 5, 7 ]>,
<identity partial perm on [ 2, 5, 7 ]>,
<identity partial perm on [ 3, 5, 7 ]>,
<identity partial perm on [ 2, 4, 6 ]>, ( 2, 4)( 6),
<identity partial perm on [ 3, 4, 5 ]>,
<identity partial perm on [ 2, 4 ]>, ( 2, 4),
<identity partial perm on [ 7 ]>, <empty partial perm> ] ]
gap> CharacterTableOfInverseSemigroup(S[ 8]);
[ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 1, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 7, 4, 3, 1, - 1, 1, 0, 0, 0, 0 ],
[ 14, 8, 6, 2, 0, - 1, 0, 0, 0, 0 ], [ 7, 4, 3, 1, 1, 1, 0, 0, 0, 0 ],
[ 10, 6, 6, 3, - 1, 0, 1, - 1, 0, 0 ], [ 10, 6, 6, 3, 1, 0, 1, 1, 0, 0 ],
[ 5, 4, 4, 3, 1, 0, 2, 0, 1, 0 ], [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ] ],
[ <identity partial perm on [ 2, 3, 4, 5, 6 ]>,
<identity partial perm on [ 1, 2, 3, 6 ]>,
<identity partial perm on [ 1, 2, 3, 5 ]>,
<identity partial perm on [ 2, 3, 6 ]>, ( 2)( 3, 6), ( 2, 3, 6),
<identity partial perm on [ 2, 3 ]>, ( 2, 3),
<identity partial perm on [ 6 ]>, <empty partial perm> ] ]
gap> CharacterTableOfInverseSemigroup(S[ 9]);
[ [ [ 1, 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 1, - 1, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 4, 0, 1, - 1, 0, 0, 0, 0, 0, 0 ], [ 4, 0, 1, 1, 0, 0, 0, 0, 0, 0 ],
[ 2, 0, 1, - 1, 1, - 1, 0, 0, 0, 0 ], [ 2, 0, 1, 1, 1, 1, 0, 0, 0, 0 ],
[ 4, - 2, 2, 0, 0, 0, 1, - 1, 0, 0 ], [ 4, 2, 2, 0, 0, 0, 1, 1, 0, 0 ],
[ 4, 0, 3, 1, 2, 0, 2, 0, 1, 0 ], [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ] ],
[ <identity partial perm on [ 1, 2, 3, 5 ]>, ( 1, 5)( 2, 3),
<identity partial perm on [ 1, 3, 5 ]>, ( 1)( 3, 5),
<identity partial perm on [ 3, 4 ]>, ( 3, 4),
<identity partial perm on [ 1, 3 ]>, ( 1, 3),
<identity partial perm on [ 3 ]>, <empty partial perm> ] ]
gap> CharacterTableOfInverseSemigroup(S[ 10]);
[ [ [ 1, 0, 0, 0, 0 ], [ 2, 1, 0, 0, 0 ], [ 3, 2, 1, 0, 0 ],
[ 4, 3, 2, 1, 0 ], [ 1, 1, 1, 1, 1 ] ],
[ <identity partial perm on [ 1, 2, 3, 4 ]>,
<identity partial perm on [ 2, 3, 5 ]>,
<identity partial perm on [ 1, 4 ]>, <identity partial perm on [ 4 ]>,
<empty partial perm> ] ]
gap> CharacterTableOfInverseSemigroup(S[ 1]);
[ [ [ 1, 0, 0, 0 ], [ 2, 1, 0, 0 ], [ 1, 1, 1, - 1 ], [ 1, 1, 1, 1 ] ],
[ <identity partial perm on [ 1, 3, 4, 5, 8, 9, 10 ]>,
<identity partial perm on [ 1, 3, 4, 6, 8 ]>,
<identity partial perm on [ 1, 3, 4, 8 ]>, ( 1)( 3)( 4, 8) ] ]
gap> CharacterTableOfInverseSemigroup(S[ 2]);
[ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 3, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 4, 4, 0, 1, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 3, 3, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 4, 3, 3, 2, 1, 2, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 4, 3, 3, 2, 1, 2, 0, 0, 0, 1, E( 3), E( 3)^ 2, 0, 0, 0, 0, 0, 0, 0, 0, 0
], [ 4, 3, 3, 2, 1, 2, 0, 0, 0, 1, E( 3)^ 2, E( 3), 0, 0, 0, 0, 0, 0,
0, 0, 0 ],
[ 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, - 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 19, 19, 20, 10, 9, 10, 4, 4, 4, 4, 1, 1, 3, - 1, 1, - 1, 1, 0, 0, 0, 0 ]
, [ 38, 38, 40, 20, 18, 20, 8, 8, 8, 8, - 1, - 1, 6, 0, 2, 0, - 1, 0, 0,
0, 0 ],
[ 19, 19, 20, 10, 9, 10, 4, 4, 4, 4, 1, 1, 3, 1, 1, 1, 1, 0, 0, 0, 0 ],
[ 15, 15, 15, 10, 10, 10, 6, 6, 6, 6, 0, 0, 6, 0, 3, - 1, 0, 1, - 1, 0, 0
], [ 15, 15, 15, 10, 10, 10, 6, 6, 6, 6, 0, 0, 6, 2, 3, 1, 0, 1, 1,
0, 0 ],
[ 6, 6, 6, 5, 5, 5, 4, 4, 4, 4, 1, 1, 4, 2, 3, 1, 0, 2, 0, 1, 0 ],
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ] ],
[ <identity partial perm on [ 3, 4, 5, 6, 7, 8 ]>,
<identity partial perm on [ 1, 2, 3, 4, 6, 7 ]>,
<identity partial perm on [ 1, 2, 4, 5, 6, 7 ]>,
<identity partial perm on [ 1, 3, 5, 6, 8 ]>,
<identity partial perm on [ 1, 2, 3, 4, 7 ]>,
<identity partial perm on [ 1, 2, 4, 5, 7 ]>,
<identity partial perm on [ 1, 3, 6, 8 ]>,
<identity partial perm on [ 1, 3, 4, 7 ]>,
<identity partial perm on [ 2, 3, 5, 7 ]>,
<identity partial perm on [ 1, 2, 4, 6 ]>, ( 1)( 2, 4, 6), ( 1)( 2, 6, 4),
<identity partial perm on [ 1, 2, 3, 4 ]>, ( 1)( 2, 4)( 3),
<identity partial perm on [ 2, 5, 7 ]>, ( 2)( 5, 7), ( 2, 5, 7),
<identity partial perm on [ 2, 5 ]>, ( 2, 5),
<identity partial perm on [ 6 ]>, <empty partial perm> ] ]
gap> CharacterTableOfInverseSemigroup(S[ 3]);
[ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 6, 6, 4, 2, 2, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 1, 0, 0, 0, 0, 1, - 1, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0 ],
[ 2, 2, 0, 0, 1, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 10, 10, 6, 6, 6, 6, 3, 3, 3, - 1, 3, 1, - 1, 0, 0 ],
[ 10, 10, 6, 6, 6, 6, 3, 3, 3, 1, 3, 1, 1, 0, 0 ],
[ 5, 5, 4, 4, 4, 4, 3, 3, 3, 1, 3, 2, 0, 1, 0 ],
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ] ],
[ <identity partial perm on [ 1, 2, 3, 4, 7 ]>,
<identity partial perm on [ 1, 2, 5, 6, 7 ]>,
<identity partial perm on [ 1, 2, 3, 7 ]>,
<identity partial perm on [ 1, 3, 6, 7 ]>,
<identity partial perm on [ 1, 5, 6, 7 ]>,
<identity partial perm on [ 2, 3, 4, 6 ]>,
<identity partial perm on [ 3, 6, 7 ]>,
<identity partial perm on [ 5, 6, 7 ]>,
<identity partial perm on [ 1, 3, 6 ]>, ( 1, 6)( 3),
<identity partial perm on [ 1, 5, 6 ]>,
<identity partial perm on [ 3, 7 ]>, ( 3, 7),
<identity partial perm on [ 1 ]>, <empty partial perm> ] ]
gap> CharacterTableOfInverseSemigroup(S[ 4]);
[ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 4, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 0, 1, 0, 0, 0, 0, 1, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 20, 10, 9, 4, 4, 3, 4, 4, 0, 1, - 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 20, 10, 9, 4, 4, 3, 4, 4, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, E( 3), E( 3)^ 2, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, E( 3)^ 2, E( 3), 0, 0, 0, 0 ],
[ 15, 10, 10, 6, 6, 6, 6, 6, - 2, 3, - 1, 3, 0, 0, 1, - 1, 0, 0 ],
[ 15, 10, 10, 6, 6, 6, 6, 6, 2, 3, 1, 3, 0, 0, 1, 1, 0, 0 ],
[ 6, 5, 5, 4, 4, 4, 4, 4, 0, 3, 1, 3, 0, 0, 2, 0, 1, 0 ],
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ] ],
[ <identity partial perm on [ 1, 3, 4, 5, 6, 7 ]>,
<identity partial perm on [ 2, 3, 5, 6, 7 ]>,
<identity partial perm on [ 1, 2, 3, 4, 6 ]>,
<identity partial perm on [ 1, 2, 4, 7 ]>,
<identity partial perm on [ 1, 4, 6, 7 ]>,
<identity partial perm on [ 2, 3, 4, 7 ]>,
<identity partial perm on [ 1, 2, 4, 6 ]>,
<identity partial perm on [ 1, 2, 5, 6 ]>, ( 1, 5)( 2, 6),
<identity partial perm on [ 1, 3, 6 ]>, ( 1)( 3, 6),
<identity partial perm on [ 2, 3, 4 ]>, ( 2, 3, 4), ( 2, 4, 3),
<identity partial perm on [ 1, 2 ]>, ( 1, 2),
<identity partial perm on [ 1 ]>, <empty partial perm> ] ]
gap> CharacterTableOfInverseSemigroup(S[ 5]);
[ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 3, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 7, 3, 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 5, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0 ]
, [ 19, 10, 4, 4, 1, 1, 1, 0, 0, 0, 0 ],
[ 19, 10, 4, 4, 1, E( 3), E( 3)^ 2, 0, 0, 0, 0 ],
[ 19, 10, 4, 4, 1, E( 3)^ 2, E( 3), 0, 0, 0, 0 ],
[ 15, 10, 6, 6, 3, 0, 0, 1, - 1, 0, 0 ],
[ 15, 10, 6, 6, 3, 0, 0, 1, 1, 0, 0 ],
[ 6, 5, 4, 4, 3, 0, 0, 2, 0, 1, 0 ],
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ] ],
[ <identity partial perm on [ 1, 2, 3, 5, 6, 7 ]>,
<identity partial perm on [ 1, 3, 4, 5, 7 ]>,
<identity partial perm on [ 1, 2, 3, 6 ]>,
<identity partial perm on [ 1, 3, 5, 6 ]>,
<identity partial perm on [ 1, 2, 6 ]>, ( 1, 2, 6), ( 1, 6, 2),
<identity partial perm on [ 1, 3 ]>, ( 1, 3),
<identity partial perm on [ 4 ]>, <empty partial perm> ] ]
gap> CharacterTableOfInverseSemigroup(S[ 6]);
[ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 2, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 3, 2, 1, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 4, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 3, 1, 1, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 5, 3, 2, 2, 2, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 4, 4, 6, 1, 2, 1, 3, 1, 2, 1, 1, 0, 0, 0, 0, 0, 1, - 1, 1, 0, 0, 0, 0 ]
, [ 8, 8, 12, 2, 4, 2, 6, 2, 4, 2, 2, 0, 0, 0, 0, 0, 2, 0, - 1, 0, 0,
0, 0 ],
[ 4, 4, 6, 1, 2, 1, 3, 1, 2, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0 ],
[ 21, 15, 15, 10, 10, 6, 6, 6, 6, 6, 6, 3, 3, 3, 3, 3, 3, - 1, 0, 1, - 1,
0, 0 ],
[ 21, 15, 15, 10, 10, 6, 6, 6, 6, 6, 6, 3, 3, 3, 3, 3, 3, 1, 0, 1, 1,
0, 0 ],
[ 7, 6, 6, 5, 5, 4, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 1, 0, 2, 0, 1, 0 ],
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ]
],
[ <identity partial perm on [ 1, 2, 5, 6, 7, 9, 10 ]>,
<identity partial perm on [ 2, 3, 7, 8, 9, 10 ]>,
<identity partial perm on [ 1, 2, 4, 6, 8, 9 ]>,
<identity partial perm on [ 1, 5, 6, 7, 10 ]>,
<identity partial perm on [ 1, 3, 4, 7, 8 ]>,
<identity partial perm on [ 3, 7, 9, 10 ]>,
<identity partial perm on [ 1, 4, 8, 9 ]>,
<identity partial perm on [ 3, 4, 6, 9 ]>,
<identity partial perm on [ 1, 3, 4, 8 ]>,
<identity partial perm on [ 1, 4, 7, 8 ]>,
<identity partial perm on [ 2, 4, 6, 8 ]>,
<identity partial perm on [ 3, 6, 9 ]>,
<identity partial perm on [ 6, 8, 9 ]>,
<identity partial perm on [ 1, 3, 7 ]>,
<identity partial perm on [ 3, 4, 6 ]>,
<identity partial perm on [ 1, 2, 4 ]>,
<identity partial perm on [ 1, 3, 4 ]>, ( 1)( 3, 4), ( 1, 3, 4),
<identity partial perm on [ 1, 3 ]>, ( 1, 3),
<identity partial perm on [ 1 ]>, <empty partial perm> ] ]
gap> CharacterTableOfInverseSemigroup(S[ 7]);
[ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 1, - 1, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, - 1, -E( 4), E( 4), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, - 1, E( 4), -E( 4), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 6, 4, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 5, 4, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 3, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 4, 2, - 2, 0, 0, 2, 1, 0, 0, 0, 1, - 1, 0, 0, 0, 0, 0 ],
[ 4, 2, 2, 0, 0, 2, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0 ],
[ 10, 4, 0, 0, 0, 5, 2, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 20, 10, - 2, 0, 0, 10, 6, 6, 3, 3, 3, - 1, 3, 1, - 1, 0, 0 ],
[ 20, 10, 2, 0, 0, 10, 6, 6, 3, 3, 3, 1, 3, 1, 1, 0, 0 ],
[ 7, 5, 1, 1, 1, 5, 4, 4, 3, 3, 3, 1, 3, 2, 0, 1, 0 ],
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ] ],
[ <identity partial perm on [ 1, 2, 4, 5, 7, 8, 9 ]>,
<identity partial perm on [ 1, 2, 4, 5, 7 ]>, ( 1)( 2, 4)( 5, 7),
( 1)( 2, 5, 4, 7), ( 1)( 2, 7, 4, 5), <identity partial perm on [ 1, 2, 4, 6, 7 ]>
, <identity partial perm on [ 1, 2, 4, 7 ]>,
<identity partial perm on [ 3, 4, 5, 7 ]>,
<identity partial perm on [ 2, 5, 7 ]>,
<identity partial perm on [ 3, 5, 7 ]>,
<identity partial perm on [ 2, 4, 6 ]>, ( 2, 4)( 6),
<identity partial perm on [ 3, 4, 5 ]>,
<identity partial perm on [ 2, 4 ]>, ( 2, 4),
<identity partial perm on [ 7 ]>, <empty partial perm> ] ]
gap> CharacterTableOfInverseSemigroup(S[ 8]);
[ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 1, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 7, 4, 3, 1, - 1, 1, 0, 0, 0, 0 ],
[ 14, 8, 6, 2, 0, - 1, 0, 0, 0, 0 ], [ 7, 4, 3, 1, 1, 1, 0, 0, 0, 0 ],
[ 10, 6, 6, 3, - 1, 0, 1, - 1, 0, 0 ], [ 10, 6, 6, 3, 1, 0, 1, 1, 0, 0 ],
[ 5, 4, 4, 3, 1, 0, 2, 0, 1, 0 ], [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ] ],
[ <identity partial perm on [ 2, 3, 4, 5, 6 ]>,
<identity partial perm on [ 1, 2, 3, 6 ]>,
<identity partial perm on [ 1, 2, 3, 5 ]>,
<identity partial perm on [ 2, 3, 6 ]>, ( 2)( 3, 6), ( 2, 3, 6),
<identity partial perm on [ 2, 3 ]>, ( 2, 3),
<identity partial perm on [ 6 ]>, <empty partial perm> ] ]
gap> CharacterTableOfInverseSemigroup(S[ 9]);
[ [ [ 1, 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 1, - 1, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 4, 0, 1, - 1, 0, 0, 0, 0, 0, 0 ], [ 4, 0, 1, 1, 0, 0, 0, 0, 0, 0 ],
[ 2, 0, 1, - 1, 1, - 1, 0, 0, 0, 0 ], [ 2, 0, 1, 1, 1, 1, 0, 0, 0, 0 ],
[ 4, - 2, 2, 0, 0, 0, 1, - 1, 0, 0 ], [ 4, 2, 2, 0, 0, 0, 1, 1, 0, 0 ],
[ 4, 0, 3, 1, 2, 0, 2, 0, 1, 0 ], [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ] ],
[ <identity partial perm on [ 1, 2, 3, 5 ]>, ( 1, 5)( 2, 3),
<identity partial perm on [ 1, 3, 5 ]>, ( 1)( 3, 5),
<identity partial perm on [ 3, 4 ]>, ( 3, 4),
<identity partial perm on [ 1, 3 ]>, ( 1, 3),
<identity partial perm on [ 3 ]>, <empty partial perm> ] ]
gap> CharacterTableOfInverseSemigroup(S[ 10]);
[ [ [ 1, 0, 0, 0, 0 ], [ 2, 1, 0, 0, 0 ], [ 3, 2, 1, 0, 0 ],
[ 4, 3, 2, 1, 0 ], [ 1, 1, 1, 1, 1 ] ],
[ <identity partial perm on [ 1, 2, 3, 4 ]>,
<identity partial perm on [ 2, 3, 5 ]>,
<identity partial perm on [ 1, 4 ]>, <identity partial perm on [ 4 ]>,
<empty partial perm> ] ]
#@else
gap> CharacterTableOfInverseSemigroup(S[ 1]);
[ [ [ 1, 0, 0, 0 ], [ 2, 1, 0, 0 ], [ 1, 1, 1, - 1 ], [ 1, 1, 1, 1 ] ],
[ <identity partial perm on [ 1, 3, 4, 5, 8, 9, 10 ]>,
<identity partial perm on [ 1, 3, 4, 6, 8 ]>,
<identity partial perm on [ 1, 3, 4, 8 ]>, ( 1)( 3)( 4, 8) ] ]
gap> CharacterTableOfInverseSemigroup(S[ 2]);
[ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 3, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 4, 4, 0, 1, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 3, 3, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 4, 3, 3, 2, 1, 2, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 4, 3, 3, 2, 1, 2, 0, 0, 0, 1, E( 3)^ 2, E( 3), 0, 0, 0, 0, 0, 0, 0, 0, 0
], [ 4, 3, 3, 2, 1, 2, 0, 0, 0, 1, E( 3), E( 3)^ 2, 0, 0, 0, 0, 0, 0,
0, 0, 0 ],
[ 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, - 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 19, 19, 20, 10, 9, 10, 4, 4, 4, 4, 1, 1, 3, - 1, 1, - 1, 1, 0, 0, 0, 0 ]
, [ 38, 38, 40, 20, 18, 20, 8, 8, 8, 8, - 1, - 1, 6, 0, 2, 0, - 1, 0, 0,
0, 0 ],
[ 19, 19, 20, 10, 9, 10, 4, 4, 4, 4, 1, 1, 3, 1, 1, 1, 1, 0, 0, 0, 0 ],
[ 15, 15, 15, 10, 10, 10, 6, 6, 6, 6, 0, 0, 6, 0, 3, - 1, 0, 1, - 1, 0, 0
], [ 15, 15, 15, 10, 10, 10, 6, 6, 6, 6, 0, 0, 6, 2, 3, 1, 0, 1, 1,
0, 0 ],
[ 6, 6, 6, 5, 5, 5, 4, 4, 4, 4, 1, 1, 4, 2, 3, 1, 0, 2, 0, 1, 0 ],
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ] ],
[ <identity partial perm on [ 3, 4, 5, 6, 7, 8 ]>,
<identity partial perm on [ 1, 2, 3, 4, 6, 7 ]>,
<identity partial perm on [ 1, 2, 4, 5, 6, 7 ]>,
<identity partial perm on [ 1, 3, 5, 6, 8 ]>,
<identity partial perm on [ 1, 2, 3, 4, 7 ]>,
<identity partial perm on [ 1, 2, 4, 5, 7 ]>,
<identity partial perm on [ 1, 3, 6, 8 ]>,
<identity partial perm on [ 1, 3, 4, 7 ]>,
<identity partial perm on [ 2, 3, 5, 7 ]>,
<identity partial perm on [ 1, 2, 4, 6 ]>, ( 1)( 2, 4, 6), ( 1)( 2, 6, 4),
<identity partial perm on [ 1, 2, 3, 4 ]>, ( 1)( 2, 4)( 3),
<identity partial perm on [ 2, 5, 7 ]>, ( 2)( 5, 7), ( 2, 5, 7),
<identity partial perm on [ 2, 5 ]>, ( 2, 5),
<identity partial perm on [ 6 ]>, <empty partial perm> ] ]
gap> CharacterTableOfInverseSemigroup(S[ 3]);
[ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 6, 6, 4, 2, 2, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 1, 0, 0, 0, 0, 1, - 1, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0 ],
[ 2, 2, 0, 0, 1, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 10, 10, 6, 6, 6, 6, 3, 3, 3, - 1, 3, 1, - 1, 0, 0 ],
[ 10, 10, 6, 6, 6, 6, 3, 3, 3, 1, 3, 1, 1, 0, 0 ],
[ 5, 5, 4, 4, 4, 4, 3, 3, 3, 1, 3, 2, 0, 1, 0 ],
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ] ],
[ <identity partial perm on [ 1, 2, 3, 4, 7 ]>,
<identity partial perm on [ 1, 2, 5, 6, 7 ]>,
<identity partial perm on [ 1, 2, 3, 7 ]>,
<identity partial perm on [ 1, 3, 6, 7 ]>,
<identity partial perm on [ 1, 5, 6, 7 ]>,
<identity partial perm on [ 2, 3, 4, 6 ]>,
<identity partial perm on [ 3, 6, 7 ]>,
<identity partial perm on [ 5, 6, 7 ]>,
<identity partial perm on [ 1, 3, 6 ]>, ( 1, 6)( 3),
<identity partial perm on [ 1, 5, 6 ]>,
<identity partial perm on [ 3, 7 ]>, ( 3, 7),
<identity partial perm on [ 1 ]>, <empty partial perm> ] ]
gap> CharacterTableOfInverseSemigroup(S[ 4]);
[ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 4, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 0, 1, 0, 0, 0, 0, 1, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 20, 10, 9, 4, 4, 3, 4, 4, 0, 1, - 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 20, 10, 9, 4, 4, 3, 4, 4, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, E( 3)^ 2, E( 3), 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, E( 3), E( 3)^ 2, 0, 0, 0, 0 ],
[ 15, 10, 10, 6, 6, 6, 6, 6, - 2, 3, - 1, 3, 0, 0, 1, - 1, 0, 0 ],
[ 15, 10, 10, 6, 6, 6, 6, 6, 2, 3, 1, 3, 0, 0, 1, 1, 0, 0 ],
[ 6, 5, 5, 4, 4, 4, 4, 4, 0, 3, 1, 3, 0, 0, 2, 0, 1, 0 ],
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ] ],
[ <identity partial perm on [ 1, 3, 4, 5, 6, 7 ]>,
<identity partial perm on [ 2, 3, 5, 6, 7 ]>,
<identity partial perm on [ 1, 2, 3, 4, 6 ]>,
<identity partial perm on [ 1, 2, 4, 7 ]>,
<identity partial perm on [ 1, 4, 6, 7 ]>,
<identity partial perm on [ 2, 3, 4, 7 ]>,
<identity partial perm on [ 1, 2, 4, 6 ]>,
<identity partial perm on [ 1, 2, 5, 6 ]>, ( 1, 5)( 2, 6),
<identity partial perm on [ 1, 3, 6 ]>, ( 1)( 3, 6),
<identity partial perm on [ 2, 3, 4 ]>, ( 2, 3, 4), ( 2, 4, 3),
<identity partial perm on [ 1, 2 ]>, ( 1, 2),
<identity partial perm on [ 1 ]>, <empty partial perm> ] ]
gap> CharacterTableOfInverseSemigroup(S[ 5]);
[ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 3, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 7, 3, 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 5, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0 ]
, [ 19, 10, 4, 4, 1, 1, 1, 0, 0, 0, 0 ],
[ 19, 10, 4, 4, 1, E( 3), E( 3)^ 2, 0, 0, 0, 0 ],
[ 19, 10, 4, 4, 1, E( 3)^ 2, E( 3), 0, 0, 0, 0 ],
[ 15, 10, 6, 6, 3, 0, 0, 1, - 1, 0, 0 ],
[ 15, 10, 6, 6, 3, 0, 0, 1, 1, 0, 0 ],
[ 6, 5, 4, 4, 3, 0, 0, 2, 0, 1, 0 ],
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ] ],
[ <identity partial perm on [ 1, 2, 3, 5, 6, 7 ]>,
<identity partial perm on [ 1, 3, 4, 5, 7 ]>,
<identity partial perm on [ 1, 2, 3, 6 ]>,
<identity partial perm on [ 1, 3, 5, 6 ]>,
<identity partial perm on [ 1, 2, 6 ]>, ( 1, 2, 6), ( 1, 6, 2),
<identity partial perm on [ 1, 3 ]>, ( 1, 3),
<identity partial perm on [ 4 ]>, <empty partial perm> ] ]
gap> CharacterTableOfInverseSemigroup(S[ 6]);
[ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 2, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 3, 2, 1, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 4, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 3, 1, 1, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 5, 3, 2, 2, 2, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 4, 4, 6, 1, 2, 1, 3, 1, 2, 1, 1, 0, 0, 0, 0, 0, 1, - 1, 1, 0, 0, 0, 0 ]
, [ 8, 8, 12, 2, 4, 2, 6, 2, 4, 2, 2, 0, 0, 0, 0, 0, 2, 0, - 1, 0, 0,
0, 0 ],
[ 4, 4, 6, 1, 2, 1, 3, 1, 2, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0 ],
[ 21, 15, 15, 10, 10, 6, 6, 6, 6, 6, 6, 3, 3, 3, 3, 3, 3, - 1, 0, 1, - 1,
0, 0 ],
[ 21, 15, 15, 10, 10, 6, 6, 6, 6, 6, 6, 3, 3, 3, 3, 3, 3, 1, 0, 1, 1,
0, 0 ],
[ 7, 6, 6, 5, 5, 4, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 1, 0, 2, 0, 1, 0 ],
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ]
],
[ <identity partial perm on [ 1, 2, 5, 6, 7, 9, 10 ]>,
<identity partial perm on [ 2, 3, 7, 8, 9, 10 ]>,
<identity partial perm on [ 1, 2, 4, 6, 8, 9 ]>,
<identity partial perm on [ 1, 5, 6, 7, 10 ]>,
<identity partial perm on [ 1, 3, 4, 7, 8 ]>,
<identity partial perm on [ 3, 7, 9, 10 ]>,
<identity partial perm on [ 1, 4, 8, 9 ]>,
<identity partial perm on [ 3, 4, 6, 9 ]>,
<identity partial perm on [ 1, 3, 4, 8 ]>,
<identity partial perm on [ 1, 4, 7, 8 ]>,
<identity partial perm on [ 2, 4, 6, 8 ]>,
<identity partial perm on [ 3, 6, 9 ]>,
<identity partial perm on [ 6, 8, 9 ]>,
<identity partial perm on [ 1, 3, 7 ]>,
<identity partial perm on [ 3, 4, 6 ]>,
<identity partial perm on [ 1, 2, 4 ]>,
<identity partial perm on [ 1, 3, 4 ]>, ( 1)( 3, 4), ( 1, 3, 4),
<identity partial perm on [ 1, 3 ]>, ( 1, 3),
<identity partial perm on [ 1 ]>, <empty partial perm> ] ]
gap> CharacterTableOfInverseSemigroup(S[ 7]);
[ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 1, - 1, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, - 1, -E( 4), E( 4), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, - 1, E( 4), -E( 4), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 6, 4, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 5, 4, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 3, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 4, 2, - 2, 0, 0, 2, 1, 0, 0, 0, 1, - 1, 0, 0, 0, 0, 0 ],
[ 4, 2, 2, 0, 0, 2, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0 ],
[ 10, 4, 0, 0, 0, 5, 2, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 20, 10, - 2, 0, 0, 10, 6, 6, 3, 3, 3, - 1, 3, 1, - 1, 0, 0 ],
[ 20, 10, 2, 0, 0, 10, 6, 6, 3, 3, 3, 1, 3, 1, 1, 0, 0 ],
[ 7, 5, 1, 1, 1, 5, 4, 4, 3, 3, 3, 1, 3, 2, 0, 1, 0 ],
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ] ],
[ <identity partial perm on [ 1, 2, 4, 5, 7, 8, 9 ]>,
<identity partial perm on [ 1, 2, 4, 5, 7 ]>, ( 1)( 2, 4)( 5, 7),
( 1)( 2, 5, 4, 7), ( 1)( 2, 7, 4, 5), <identity partial perm on [ 1, 2, 4, 6, 7 ]>
, <identity partial perm on [ 1, 2, 4, 7 ]>,
<identity partial perm on [ 3, 4, 5, 7 ]>,
<identity partial perm on [ 2, 5, 7 ]>,
<identity partial perm on [ 3, 5, 7 ]>,
<identity partial perm on [ 2, 4, 6 ]>, ( 2, 4)( 6),
<identity partial perm on [ 3, 4, 5 ]>,
<identity partial perm on [ 2, 4 ]>, ( 2, 4),
<identity partial perm on [ 7 ]>, <empty partial perm> ] ]
gap> CharacterTableOfInverseSemigroup(S[ 8]);
[ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 1, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 7, 4, 3, 1, - 1, 1, 0, 0, 0, 0 ],
[ 14, 8, 6, 2, 0, - 1, 0, 0, 0, 0 ], [ 7, 4, 3, 1, 1, 1, 0, 0, 0, 0 ],
[ 10, 6, 6, 3, - 1, 0, 1, - 1, 0, 0 ], [ 10, 6, 6, 3, 1, 0, 1, 1, 0, 0 ],
[ 5, 4, 4, 3, 1, 0, 2, 0, 1, 0 ], [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ] ],
[ <identity partial perm on [ 2, 3, 4, 5, 6 ]>,
<identity partial perm on [ 1, 2, 3, 6 ]>,
<identity partial perm on [ 1, 2, 3, 5 ]>,
<identity partial perm on [ 2, 3, 6 ]>, ( 2)( 3, 6), ( 2, 3, 6),
<identity partial perm on [ 2, 3 ]>, ( 2, 3),
<identity partial perm on [ 6 ]>, <empty partial perm> ] ]
gap> CharacterTableOfInverseSemigroup(S[ 9]);
[ [ [ 1, 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 1, - 1, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 4, 0, 1, - 1, 0, 0, 0, 0, 0, 0 ], [ 4, 0, 1, 1, 0, 0, 0, 0, 0, 0 ],
[ 2, 0, 1, - 1, 1, - 1, 0, 0, 0, 0 ], [ 2, 0, 1, 1, 1, 1, 0, 0, 0, 0 ],
[ 4, - 2, 2, 0, 0, 0, 1, - 1, 0, 0 ], [ 4, 2, 2, 0, 0, 0, 1, 1, 0, 0 ],
[ 4, 0, 3, 1, 2, 0, 2, 0, 1, 0 ], [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ] ],
[ <identity partial perm on [ 1, 2, 3, 5 ]>, ( 1, 5)( 2, 3),
<identity partial perm on [ 1, 3, 5 ]>, ( 1)( 3, 5),
<identity partial perm on [ 3, 4 ]>, ( 3, 4),
<identity partial perm on [ 1, 3 ]>, ( 1, 3),
<identity partial perm on [ 3 ]>, <empty partial perm> ] ]
gap> CharacterTableOfInverseSemigroup(S[ 10]);
[ [ [ 1, 0, 0, 0, 0 ], [ 2, 1, 0, 0, 0 ], [ 3, 2, 1, 0, 0 ],
[ 4, 3, 2, 1, 0 ], [ 1, 1, 1, 1, 1 ] ],
[ <identity partial perm on [ 1, 2, 3, 4 ]>,
<identity partial perm on [ 2, 3, 5 ]>,
<identity partial perm on [ 1, 4 ]>, <identity partial perm on [ 4 ]>,
<empty partial perm> ] ]
gap> CharacterTableOfInverseSemigroup(S[ 1]);
[ [ [ 1, 0, 0, 0 ], [ 2, 1, 0, 0 ], [ 1, 1, 1, - 1 ], [ 1, 1, 1, 1 ] ],
[ <identity partial perm on [ 1, 3, 4, 5, 8, 9, 10 ]>,
<identity partial perm on [ 1, 3, 4, 6, 8 ]>,
<identity partial perm on [ 1, 3, 4, 8 ]>, ( 1)( 3)( 4, 8) ] ]
gap> CharacterTableOfInverseSemigroup(S[ 2]);
[ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 3, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 4, 4, 0, 1, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 3, 3, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 4, 3, 3, 2, 1, 2, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 4, 3, 3, 2, 1, 2, 0, 0, 0, 1, E( 3)^ 2, E( 3), 0, 0, 0, 0, 0, 0, 0, 0, 0
], [ 4, 3, 3, 2, 1, 2, 0, 0, 0, 1, E( 3), E( 3)^ 2, 0, 0, 0, 0, 0, 0,
0, 0, 0 ],
[ 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, - 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 19, 19, 20, 10, 9, 10, 4, 4, 4, 4, 1, 1, 3, - 1, 1, - 1, 1, 0, 0, 0, 0 ]
, [ 38, 38, 40, 20, 18, 20, 8, 8, 8, 8, - 1, - 1, 6, 0, 2, 0, - 1, 0, 0,
0, 0 ],
[ 19, 19, 20, 10, 9, 10, 4, 4, 4, 4, 1, 1, 3, 1, 1, 1, 1, 0, 0, 0, 0 ],
[ 15, 15, 15, 10, 10, 10, 6, 6, 6, 6, 0, 0, 6, 0, 3, - 1, 0, 1, - 1, 0, 0
], [ 15, 15, 15, 10, 10, 10, 6, 6, 6, 6, 0, 0, 6, 2, 3, 1, 0, 1, 1,
0, 0 ],
[ 6, 6, 6, 5, 5, 5, 4, 4, 4, 4, 1, 1, 4, 2, 3, 1, 0, 2, 0, 1, 0 ],
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ] ],
[ <identity partial perm on [ 3, 4, 5, 6, 7, 8 ]>,
<identity partial perm on [ 1, 2, 3, 4, 6, 7 ]>,
<identity partial perm on [ 1, 2, 4, 5, 6, 7 ]>,
<identity partial perm on [ 1, 3, 5, 6, 8 ]>,
<identity partial perm on [ 1, 2, 3, 4, 7 ]>,
<identity partial perm on [ 1, 2, 4, 5, 7 ]>,
<identity partial perm on [ 1, 3, 6, 8 ]>,
<identity partial perm on [ 1, 3, 4, 7 ]>,
<identity partial perm on [ 2, 3, 5, 7 ]>,
<identity partial perm on [ 1, 2, 4, 6 ]>, ( 1)( 2, 4, 6), ( 1)( 2, 6, 4),
<identity partial perm on [ 1, 2, 3, 4 ]>, ( 1)( 2, 4)( 3),
<identity partial perm on [ 2, 5, 7 ]>, ( 2)( 5, 7), ( 2, 5, 7),
<identity partial perm on [ 2, 5 ]>, ( 2, 5),
<identity partial perm on [ 6 ]>, <empty partial perm> ] ]
gap> CharacterTableOfInverseSemigroup(S[ 3]);
[ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 6, 6, 4, 2, 2, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 1, 0, 0, 0, 0, 1, - 1, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0 ],
[ 2, 2, 0, 0, 1, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 10, 10, 6, 6, 6, 6, 3, 3, 3, - 1, 3, 1, - 1, 0, 0 ],
[ 10, 10, 6, 6, 6, 6, 3, 3, 3, 1, 3, 1, 1, 0, 0 ],
[ 5, 5, 4, 4, 4, 4, 3, 3, 3, 1, 3, 2, 0, 1, 0 ],
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ] ],
[ <identity partial perm on [ 1, 2, 3, 4, 7 ]>,
<identity partial perm on [ 1, 2, 5, 6, 7 ]>,
<identity partial perm on [ 1, 2, 3, 7 ]>,
<identity partial perm on [ 1, 3, 6, 7 ]>,
<identity partial perm on [ 1, 5, 6, 7 ]>,
<identity partial perm on [ 2, 3, 4, 6 ]>,
<identity partial perm on [ 3, 6, 7 ]>,
<identity partial perm on [ 5, 6, 7 ]>,
<identity partial perm on [ 1, 3, 6 ]>, ( 1, 6)( 3),
<identity partial perm on [ 1, 5, 6 ]>,
<identity partial perm on [ 3, 7 ]>, ( 3, 7),
<identity partial perm on [ 1 ]>, <empty partial perm> ] ]
gap> CharacterTableOfInverseSemigroup(S[ 4]);
[ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 4, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 0, 1, 0, 0, 0, 0, 1, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 20, 10, 9, 4, 4, 3, 4, 4, 0, 1, - 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 20, 10, 9, 4, 4, 3, 4, 4, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, E( 3)^ 2, E( 3), 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, E( 3), E( 3)^ 2, 0, 0, 0, 0 ],
[ 15, 10, 10, 6, 6, 6, 6, 6, - 2, 3, - 1, 3, 0, 0, 1, - 1, 0, 0 ],
[ 15, 10, 10, 6, 6, 6, 6, 6, 2, 3, 1, 3, 0, 0, 1, 1, 0, 0 ],
[ 6, 5, 5, 4, 4, 4, 4, 4, 0, 3, 1, 3, 0, 0, 2, 0, 1, 0 ],
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ] ],
[ <identity partial perm on [ 1, 3, 4, 5, 6, 7 ]>,
<identity partial perm on [ 2, 3, 5, 6, 7 ]>,
<identity partial perm on [ 1, 2, 3, 4, 6 ]>,
<identity partial perm on [ 1, 2, 4, 7 ]>,
<identity partial perm on [ 1, 4, 6, 7 ]>,
<identity partial perm on [ 2, 3, 4, 7 ]>,
<identity partial perm on [ 1, 2, 4, 6 ]>,
<identity partial perm on [ 1, 2, 5, 6 ]>, ( 1, 5)( 2, 6),
<identity partial perm on [ 1, 3, 6 ]>, ( 1)( 3, 6),
<identity partial perm on [ 2, 3, 4 ]>, ( 2, 3, 4), ( 2, 4, 3),
<identity partial perm on [ 1, 2 ]>, ( 1, 2),
<identity partial perm on [ 1 ]>, <empty partial perm> ] ]
gap> CharacterTableOfInverseSemigroup(S[ 5]);
[ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 3, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 7, 3, 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 5, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0 ]
, [ 19, 10, 4, 4, 1, 1, 1, 0, 0, 0, 0 ],
[ 19, 10, 4, 4, 1, E( 3), E( 3)^ 2, 0, 0, 0, 0 ],
[ 19, 10, 4, 4, 1, E( 3)^ 2, E( 3), 0, 0, 0, 0 ],
[ 15, 10, 6, 6, 3, 0, 0, 1, - 1, 0, 0 ],
[ 15, 10, 6, 6, 3, 0, 0, 1, 1, 0, 0 ],
[ 6, 5, 4, 4, 3, 0, 0, 2, 0, 1, 0 ],
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ] ],
[ <identity partial perm on [ 1, 2, 3, 5, 6, 7 ]>,
<identity partial perm on [ 1, 3, 4, 5, 7 ]>,
<identity partial perm on [ 1, 2, 3, 6 ]>,
<identity partial perm on [ 1, 3, 5, 6 ]>,
<identity partial perm on [ 1, 2, 6 ]>, ( 1, 2, 6), ( 1, 6, 2),
<identity partial perm on [ 1, 3 ]>, ( 1, 3),
<identity partial perm on [ 4 ]>, <empty partial perm> ] ]
gap> CharacterTableOfInverseSemigroup(S[ 6]);
[ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 2, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 3, 2, 1, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 4, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 3, 1, 1, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 5, 3, 2, 2, 2, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 4, 4, 6, 1, 2, 1, 3, 1, 2, 1, 1, 0, 0, 0, 0, 0, 1, - 1, 1, 0, 0, 0, 0 ]
, [ 8, 8, 12, 2, 4, 2, 6, 2, 4, 2, 2, 0, 0, 0, 0, 0, 2, 0, - 1, 0, 0,
0, 0 ],
[ 4, 4, 6, 1, 2, 1, 3, 1, 2, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0 ],
[ 21, 15, 15, 10, 10, 6, 6, 6, 6, 6, 6, 3, 3, 3, 3, 3, 3, - 1, 0, 1, - 1,
0, 0 ],
[ 21, 15, 15, 10, 10, 6, 6, 6, 6, 6, 6, 3, 3, 3, 3, 3, 3, 1, 0, 1, 1,
0, 0 ],
[ 7, 6, 6, 5, 5, 4, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 1, 0, 2, 0, 1, 0 ],
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ]
],
[ <identity partial perm on [ 1, 2, 5, 6, 7, 9, 10 ]>,
<identity partial perm on [ 2, 3, 7, 8, 9, 10 ]>,
<identity partial perm on [ 1, 2, 4, 6, 8, 9 ]>,
<identity partial perm on [ 1, 5, 6, 7, 10 ]>,
<identity partial perm on [ 1, 3, 4, 7, 8 ]>,
<identity partial perm on [ 3, 7, 9, 10 ]>,
<identity partial perm on [ 1, 4, 8, 9 ]>,
<identity partial perm on [ 3, 4, 6, 9 ]>,
<identity partial perm on [ 1, 3, 4, 8 ]>,
<identity partial perm on [ 1, 4, 7, 8 ]>,
<identity partial perm on [ 2, 4, 6, 8 ]>,
<identity partial perm on [ 3, 6, 9 ]>,
<identity partial perm on [ 6, 8, 9 ]>,
<identity partial perm on [ 1, 3, 7 ]>,
<identity partial perm on [ 3, 4, 6 ]>,
<identity partial perm on [ 1, 2, 4 ]>,
<identity partial perm on [ 1, 3, 4 ]>, ( 1)( 3, 4), ( 1, 3, 4),
<identity partial perm on [ 1, 3 ]>, ( 1, 3),
<identity partial perm on [ 1 ]>, <empty partial perm> ] ]
gap> CharacterTableOfInverseSemigroup(S[ 7]);
[ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 1, - 1, - 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, - 1, -E( 4), E( 4), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, - 1, E( 4), -E( 4), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 6, 4, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 5, 4, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 3, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 4, 2, - 2, 0, 0, 2, 1, 0, 0, 0, 1, - 1, 0, 0, 0, 0, 0 ],
[ 4, 2, 2, 0, 0, 2, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0 ],
[ 10, 4, 0, 0, 0, 5, 2, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 20, 10, - 2, 0, 0, 10, 6, 6, 3, 3, 3, - 1, 3, 1, - 1, 0, 0 ],
[ 20, 10, 2, 0, 0, 10, 6, 6, 3, 3, 3, 1, 3, 1, 1, 0, 0 ],
[ 7, 5, 1, 1, 1, 5, 4, 4, 3, 3, 3, 1, 3, 2, 0, 1, 0 ],
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ] ],
[ <identity partial perm on [ 1, 2, 4, 5, 7, 8, 9 ]>,
<identity partial perm on [ 1, 2, 4, 5, 7 ]>, ( 1)( 2, 4)( 5, 7),
( 1)( 2, 5, 4, 7), ( 1)( 2, 7, 4, 5), <identity partial perm on [ 1, 2, 4, 6, 7 ]>
, <identity partial perm on [ 1, 2, 4, 7 ]>,
<identity partial perm on [ 3, 4, 5, 7 ]>,
<identity partial perm on [ 2, 5, 7 ]>,
<identity partial perm on [ 3, 5, 7 ]>,
<identity partial perm on [ 2, 4, 6 ]>, ( 2, 4)( 6),
<identity partial perm on [ 3, 4, 5 ]>,
<identity partial perm on [ 2, 4 ]>, ( 2, 4),
<identity partial perm on [ 7 ]>, <empty partial perm> ] ]
gap> CharacterTableOfInverseSemigroup(S[ 8]);
[ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 1, 1, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 0, 1, 0, 0, 0, 0, 0, 0, 0 ], [ 7, 4, 3, 1, - 1, 1, 0, 0, 0, 0 ],
[ 14, 8, 6, 2, 0, - 1, 0, 0, 0, 0 ], [ 7, 4, 3, 1, 1, 1, 0, 0, 0, 0 ],
[ 10, 6, 6, 3, - 1, 0, 1, - 1, 0, 0 ], [ 10, 6, 6, 3, 1, 0, 1, 1, 0, 0 ],
[ 5, 4, 4, 3, 1, 0, 2, 0, 1, 0 ], [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ] ],
[ <identity partial perm on [ 2, 3, 4, 5, 6 ]>,
<identity partial perm on [ 1, 2, 3, 6 ]>,
<identity partial perm on [ 1, 2, 3, 5 ]>,
<identity partial perm on [ 2, 3, 6 ]>, ( 2)( 3, 6), ( 2, 3, 6),
<identity partial perm on [ 2, 3 ]>, ( 2, 3),
<identity partial perm on [ 6 ]>, <empty partial perm> ] ]
gap> CharacterTableOfInverseSemigroup(S[ 9]);
[ [ [ 1, 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 1, - 1, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 4, 0, 1, - 1, 0, 0, 0, 0, 0, 0 ], [ 4, 0, 1, 1, 0, 0, 0, 0, 0, 0 ],
[ 2, 0, 1, - 1, 1, - 1, 0, 0, 0, 0 ], [ 2, 0, 1, 1, 1, 1, 0, 0, 0, 0 ],
[ 4, - 2, 2, 0, 0, 0, 1, - 1, 0, 0 ], [ 4, 2, 2, 0, 0, 0, 1, 1, 0, 0 ],
[ 4, 0, 3, 1, 2, 0, 2, 0, 1, 0 ], [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ] ],
[ <identity partial perm on [ 1, 2, 3, 5 ]>, ( 1, 5)( 2, 3),
<identity partial perm on [ 1, 3, 5 ]>, ( 1)( 3, 5),
<identity partial perm on [ 3, 4 ]>, ( 3, 4),
<identity partial perm on [ 1, 3 ]>, ( 1, 3),
<identity partial perm on [ 3 ]>, <empty partial perm> ] ]
gap> CharacterTableOfInverseSemigroup(S[ 10]);
[ [ [ 1, 0, 0, 0, 0 ], [ 2, 1, 0, 0, 0 ], [ 3, 2, 1, 0, 0 ],
[ 4, 3, 2, 1, 0 ], [ 1, 1, 1, 1, 1 ] ],
[ <identity partial perm on [ 1, 2, 3, 4 ]>,
<identity partial perm on [ 2, 3, 5 ]>,
<identity partial perm on [ 1, 4 ]>, <identity partial perm on [ 4 ]>,
<empty partial perm> ] ]
#@fi
# attrinv: NaturalPartialOrder (for a semigroup), works, 1/ 1
gap> S := InverseSemigroup([Bipartition([[ 1, - 3], [ 2, - 1], [ 3, 4, - 2, - 4]]),
> Bipartition([[ 1, - 1], [ 2, - 3], [ 3, - 2], [ 4, - 4]])]);
<inverse block bijection semigroup of degree 4 with 2 generators>
gap> S := AsSemigroup(IsTransformationSemigroup, S);
<transformation semigroup of size 20, degree 20 with 3 generators>
gap> n := Size(S);;
gap> elts := Elements(S);;
gap> NaturalPartialOrder(S);
[ [ 2, 8, 9, 15, 16, 19 ], [ 9, 16, 19 ], [ 4, 9, 11 ], [ 9 ], [ 9, 16, 18 ],
[ 5, 9, 10, 14, 16, 18 ], [ 9, 13, 20 ], [ 9 ], [ ], [ 9 ], [ 9 ],
[ 9, 11, 13 ], [ 9 ], [ 9, 10, 16 ], [ 8, 9, 16 ], [ 9 ], [ 4, 9, 20 ],
[ 9 ], [ 9 ], [ 9 ] ]
gap> List([ 1 .. n],
> i -> Filtered([ 1 .. n],
> j -> i <> j and ForAny(Idempotents(S),
> e -> e * elts[i] = elts[j])));
[ [ 2, 8, 9, 15, 16, 19 ], [ 9, 16, 19 ], [ 4, 9, 11 ], [ 9 ], [ 9, 16, 18 ],
[ 5, 9, 10, 14, 16, 18 ], [ 9, 13, 20 ], [ 9 ], [ ], [ 9 ], [ 9 ],
[ 9, 11, 13 ], [ 9 ], [ 9, 10, 16 ], [ 8, 9, 16 ], [ 9 ], [ 4, 9, 20 ],
[ 9 ], [ 9 ], [ 9 ] ]
gap> last = last2;
true
# attrinv: NaturalPartialOrder (for a semigroup), works, 2
gap> S := Semigroup(SymmetricInverseMonoid( 3), rec(acting := true));;
gap> es := IdempotentGeneratedSubsemigroup(S);;
gap> n := Size(es);;
gap> elts := Elements(es);
[ <empty partial perm>, <identity partial perm on [ 1 ]>,
<identity partial perm on [ 2 ]>, <identity partial perm on [ 1, 2 ]>,
<identity partial perm on [ 3 ]>, <identity partial perm on [ 2, 3 ]>,
<identity partial perm on [ 1, 3 ]>, <identity partial perm on [ 1, 2, 3 ]>
]
gap> NaturalPartialOrder(es);
[ [ ], [ 1 ], [ 1 ], [ 1, 2, 3 ], [ 1 ], [ 1, 3, 5 ], [ 1, 2, 5 ],
[ 1, 2, 3, 4, 5, 6, 7 ] ]
gap> List([ 1 .. n],
> i -> Filtered([ 1 .. n], j -> elts[j] = elts[j] * elts[i] and i <> j));
[ [ ], [ 1 ], [ 1 ], [ 1, 2, 3 ], [ 1 ], [ 1, 3, 5 ], [ 1, 2, 5 ],
[ 1, 2, 3, 4, 5, 6, 7 ] ]
gap> last = last2;
true
# attrinv: NaturalPartialOrder (for a semigroup), works, 3
gap> S := Semigroup(SymmetricInverseMonoid( 3), rec(acting := true));;
gap> es := IdempotentGeneratedSubsemigroup(S);;
gap> es := AsSemigroup(IsBlockBijectionSemigroup, es);;
gap> n := Size(es);;
gap> elts := Elements(es);;
gap> NaturalPartialOrder(es);
[ [ ], [ 1 ], [ 1 ], [ 1 ], [ 1, 2, 3 ], [ 1, 2, 4 ], [ 1, 3, 4 ],
[ 1, 2, 3, 4, 5, 6, 7 ] ]
gap> List([ 1 .. n],
> i -> Filtered([ 1 .. n], j -> elts[j] = elts[j] * elts[i] and i <> j));
[ [ ], [ 1 ], [ 1 ], [ 1 ], [ 1, 2, 3 ], [ 1, 2, 4 ], [ 1, 3, 4 ],
[ 1, 2, 3, 4, 5, 6, 7 ] ]
gap> last = last2;
true
# attrinv: NaturalPartialOrder (for a semigroup), error, 1/ 2
gap> S := Semigroup(
> [Matrix(IsTropicalMinPlusMatrix,
> [[infinity, 0, infinity, 1, 1, infinity, 3, 2, 3],
> [ 3, 1, 1, infinity, 1, 1, 1, 1, 1], [ 0, 3, 0, 1, 1, 3, 0, infinity, 1],
> [ 0, 0, 1, infinity, infinity, 3, 3, 2, 1], [ 1, 1, 0, 3, 0, 3, 0, 0, 3],
> [ 0, 2, 3, 1, 0, 0, infinity, 3, infinity],
> [ 1, 2, 3, 3, 1, 2, infinity, infinity, 3],
> [ 1, 1, infinity, 3, 3, 1, 1, 1, 1], [ 1, 2, 0, infinity, 0, 0, 1, 1, 2]],
> 3)]);
<commutative semigroup of 9x9 tropical min-plus matrices with 1 generator>
gap> NaturalPartialOrder(S);
Error, the argument (a semigroup) is not an inverse semigroup
# attrinv: NaturalPartialOrder (for a semigroup), error, 2/ 2
gap> NaturalPartialOrder(FreeInverseSemigroup( 2));
Error, the argument (a semigroup) is not finite
# attrinv: NaturalLeqInverseSemigroup (for a semigroup), error, 1/ 2
gap> S := Semigroup([
> PBR(
> [[- 4, - 3, - 2, - 1, 1, 4, 5, 6], [- 6, - 5, - 4, - 3, - 2, 2, 6],
> [- 6, - 4, - 3, - 1, 1, 2, 4, 5, 6], [- 6, 2, 3, 4], [- 4, - 2, 3, 6],
> [- 6, - 3, 1, 3, 4, 6]],
> [[- 5, - 2, - 1, 3, 4], [- 5, - 2, 1, 3, 5],
> [- 6, - 4, - 2, 2, 3, 4, 6], [- 5, - 3, - 1, 2, 4, 6], [- 6, - 3, 1, 2, 3, 4, 6],
> [- 6, - 3, 2, 6]]),
> PBR(
> [[- 6, - 5, - 3, - 2, - 1, 3, 6], [- 6, - 2, 1, 2, 5], [- 6, - 5, - 4, - 1, 1, 6],
> [- 6, - 5, - 4, - 2, - 1, 2, 5], [- 6, - 2, - 1, 1, 2, 4, 5], [- 6, - 5, 3, 4, 6]],
> [[- 2, 1, 2, 3, 5, 6], [- 6, - 5, - 4, - 3, - 2, 1, 3, 5],
> [- 6, - 4, - 3, - 1, 2, 5, 6], [- 5, - 2, 3, 4, 5],
> [- 6, - 5, - 4, - 3, - 2, 1, 2, 3, 5, 6], [- 4, 2, 3, 4, 5, 6]])]);
<pbr semigroup of degree 6 with 2 generators>
gap> NaturalLeqInverseSemigroup(S);
Error, the argument (a semigroup) is not an inverse semigroup
# attrinv: NaturalLeqInverseSemigroup (for a semigroup), error, 2/ 2
gap> NaturalLeqInverseSemigroup(FreeInverseSemigroup( 2));
Error, the argument (a semigroup) is not finite
# attrinv: IsGreensDGreaterThanFunc (for an inverse op acting semigroup), 1/ 1
gap> S := InverseSemigroup(
> [Bipartition([[ 1, - 3], [ 2, - 1], [ 3, 4, 5, - 2, - 4, - 5]]),
> Bipartition([[ 1, - 1], [ 2, - 3], [ 3, - 4], [ 4, 5, - 2, - 5]])]);
<inverse block bijection semigroup of degree 5 with 2 generators>
gap> Size(S);
39
gap> foo := IsGreensDGreaterThanFunc(S);;
gap> foo(S. 1, S. 2);
false
gap> foo(S. 2, S. 1);
true
gap> foo(S. 1, S. 1);
false
# attrinv: PrimitiveIdempotents, inverse, 1/ 2
gap> S := InverseSemigroup([PartialPerm([ 1, 2], [ 3, 1]),
> PartialPerm([ 1, 2, 3], [ 1, 3, 4])]);;
gap> Set(PrimitiveIdempotents(S));
[ <identity partial perm on [ 1 ]>, <identity partial perm on [ 2 ]>,
<identity partial perm on [ 3 ]>, <identity partial perm on [ 4 ]> ]
# attrinv: PrimitiveIdempotents, inverse, 2/ 2
gap> S := InverseSemigroup(
> [PartialPerm([ 1, 2, 3, 5, 6, 11, 12], [ 4, 3, 7, 5, 1, 11, 12]),
> PartialPerm([ 1, 3, 4, 5, 6, 7, 11, 12], [ 6, 7, 5, 3, 1, 4, 11, 12]),
> PartialPerm([ 11, 12], [ 12, 11])]);;
gap> PrimitiveIdempotents(S);
[ <identity partial perm on [ 11, 12 ]> ]
# attrinv: PrimitiveIdempotents, semigroup, error, 1/ 2
gap> PrimitiveIdempotents(FreeSemigroup( 2));
Error, the argument (a semigroup) is not finite
# attrinv: PrimitiveIdempotents, semigroup, error, 2/ 2
gap> PrimitiveIdempotents(FreeBand( 2));
Error, the argument (a semigroup) is not an inverse semigroup
# attrinv: PrimitiveIdempotents, transformation semigroups
gap> S := InverseSemigroup([
> Bipartition([[ 1, - 1, - 2], [ 2, 3, - 3], [ 4, - 4]]),
> Bipartition([[ 1, 2, 3, - 4], [ 4, - 1, - 2, - 3]])]);
<inverse block bijection semigroup of degree 4 with 2 generators>
gap> PrimitiveIdempotents(S);
[ <block bijection: [ 1, 2, 3, - 1, - 2, - 3 ], [ 4, - 4 ]> ]
gap> S := AsSemigroup(IsTransformationSemigroup, S);
<transformation semigroup of size 6, degree 7 with 3 generators>
gap> PrimitiveIdempotents(S);
[ Transformation( [ 4, 2, 4, 4, 4, 4, 4 ] ) ]
#
gap> S := InverseSemigroup([
> PartialPerm([ 1, 2, 3, 5], [ 2, 5, 4, 1]),
> PartialPerm([ 1, 2, 4], [ 3, 4, 2]),
> PartialPerm([ 1, 2, 3, 5], [ 1, 4, 3, 2])]);
<inverse partial perm semigroup of rank 5 with 3 generators>
gap> x := ShallowCopy(PrimitiveIdempotents(S));;
gap> Sort(x);
gap> x;
[ <identity partial perm on [ 1 ]>, <identity partial perm on [ 2 ]>,
<identity partial perm on [ 3 ]>, <identity partial perm on [ 4 ]>,
<identity partial perm on [ 5 ]> ]
gap> T := AsSemigroup(IsBlockBijectionSemigroup, S);
<inverse block bijection semigroup of degree 6 with 3 generators>
gap> x := ShallowCopy(PrimitiveIdempotents(T));;
gap> Sort(x);
gap> x;
[ <block bijection: [ 1, 2, 3, 4, 6, - 1, - 2, - 3, - 4, - 6 ], [ 5, - 5 ]>,
<block bijection: [ 1, 2, 3, 5, 6, - 1, - 2, - 3, - 5, - 6 ], [ 4, - 4 ]>,
<block bijection: [ 1, 2, 4, 5, 6, - 1, - 2, - 4, - 5, - 6 ], [ 3, - 3 ]>,
<block bijection: [ 1, 3, 4, 5, 6, - 1, - 3, - 4, - 5, - 6 ], [ 2, - 2 ]>,
<block bijection: [ 1, - 1 ], [ 2, 3, 4, 5, 6, - 2, - 3, - 4, - 5, - 6 ]> ]
gap> T := AsSemigroup(IsTransformationSemigroup, S);
<transformation semigroup of degree 6 with 6 generators>
gap> x := ShallowCopy(PrimitiveIdempotents(T));;
gap> Sort(x);
gap> x;
[ Transformation( [ 1, 6, 6, 6, 6, 6 ] ),
Transformation( [ 6, 2, 6, 6, 6, 6 ] ),
Transformation( [ 6, 6, 3, 6, 6, 6 ] ),
Transformation( [ 6, 6, 6, 4, 6, 6 ] ),
Transformation( [ 6, 6, 6, 6, 5, 6 ] ) ]
# attrinv: IsJoinIrreducible, 1/ 4
gap> S := InverseSemigroup([
> PartialPerm([ 1, 2, 3, 4], [ 4, 1, 2, 6]),
> PartialPerm([ 1, 2, 3, 4], [ 5, 7, 1, 6]),
> PartialPerm([ 1, 2, 3, 5], [ 5, 2, 7, 3]),
> PartialPerm([ 1, 2, 3, 6, 7], [ 1, 3, 4, 7, 5]),
> PartialPerm([ 1, 2, 3, 4, 5, 7], [ 3, 2, 4, 6, 1, 5])]);;
gap> I := SemigroupIdeal(S,
> PartialPerm([ 1, 3, 4, 5, 7], [ 1, 3, 4, 5, 7]));;
gap> x := PartialPerm([ 1, 2, 4, 6], [ 2, 3, 1, 4]);;
gap> x in S;
true
gap> IsJoinIrreducible(S, x);
false
gap> x in I;
true
gap> IsJoinIrreducible(S, RandomBipartition( 1));
Error, the 2nd argument (a mult. elt.) does not belong to the 1st argument (an\
inverse semigroup)
gap> IsJoinIrreducible(S, MultiplicativeZero(S));
false
# attrinv: IsJoinIrreducible, 2/ 4
gap> S := InverseSemigroup(
> [PartialPerm([ 1, 2, 3, 5, 6, 11, 12], [ 4, 3, 7, 5, 1, 11, 12]),
> PartialPerm([ 1, 3, 4, 5, 6, 7, 11, 12], [ 6, 7, 5, 3, 1, 4, 11, 12]),
> PartialPerm([ 11, 12], [ 12, 11])]);;
gap> IsJoinIrreducible(S, PrimitiveIdempotents(S)[ 1]);
true
# attrinv: IsJoinIrreducible, 3/ 4
gap> S := DualSymmetricInverseMonoid( 3);
<inverse block bijection monoid of degree 3 with 3 generators>
gap> x := Bipartition([[ 1, 2, - 1, - 2], [ 3, - 3]]);;
gap> IsJoinIrreducible(S, x);
true
# attrinv: IsJoinIrreducible, 4/ 4
gap> S := InverseSemigroup([
> PartialPerm([ 1, 2, 4, 6], [ 2, 1, 4, 6]),
> PartialPerm([ 1, 2, 3, 4], [ 4, 1, 2, 6]),
> PartialPerm([ 1, 2, 3, 4], [ 5, 7, 1, 6]),
> PartialPerm([ 1, 2, 3, 5], [ 5, 2, 7, 3]),
> PartialPerm([ 1, 2, 3, 6, 7], [ 1, 3, 4, 7, 5]),
> PartialPerm([ 1, 2, 3, 4, 5, 7], [ 3, 2, 4, 6, 1, 5])]);;
gap> x := PartialPerm([ 1, 2, 4, 6], [ 2, 3, 1, 4]);;
gap> IsJoinIrreducible(S, x);
false
# attrinv: IsMajorantlyClosed, 1/ 1
gap> S := DualSymmetricInverseMonoid( 3);
<inverse block bijection monoid of degree 3 with 3 generators>
gap> Size(S);
25
gap> T := InverseMonoid([Bipartition([[ 1, - 1], [ 2, 3, - 2, - 3]]),
> Bipartition([[ 1, - 2], [ 2, 3, - 1, - 3]])]);
<inverse block bijection monoid of degree 3 with 2 generators>
gap> IsMajorantlyClosed(S, T);
false
gap> IsMajorantlyClosed(S, S);
true
gap> IsMajorantlyClosed(T, S);
Error, the 2nd argument (an inverse semigroup) is not a subsemigroup of the 1s\
t argument (an inverse semigroup)
gap> IsMajorantlyClosed(S, Elements(T));
false
gap> IsMajorantlyClosed(S, Elements(S));
true
gap> IsMajorantlyClosed(T, Elements(S));
Error, the 2nd argument (a mult. elt. coll) is not a subset of the 1st argumen\
t (an inverse semigroup)
gap> IsMajorantlyClosed(S, [One(S)]);
true
# attrinv: JoinIrreducibleDClasses, partial perms, 1
gap> S := InverseSemigroup([PartialPerm([ 1, 2, 3, 4], [ 2, 4, 1, 5]),
> PartialPerm([ 1, 3, 5], [ 5, 1, 3])]);;
gap> JoinIrreducibleDClasses(S)[ 1] = DClass(S, PartialPerm([ 3], [ 3]));
true
gap> S := InverseSemigroup(S, rec(acting := false));;
gap> JoinIrreducibleDClasses(S)[ 1] = DClass(S, PartialPerm([ 3], [ 3]));
true
# attrinv: JoinIrreducibleDClasses, partial perms, 2
gap> S := InverseSemigroup([PartialPerm([ 1, 2, 3, 4], [ 2, 4, 1, 5]),
> PartialPerm([ 1, 3, 5], [ 5, 1, 3])]);;
gap> JoinIrreducibleDClasses(S)[ 1] = DClass(S, PartialPerm([ 3], [ 3]));
true
# attrinv: JoinIrreducibleDClasses, partial perms, 3
gap> S := Semigroup(
> [PartialPerm([ 1, 2, 3, 4], [ 1, 2, 3, 4]),
> PartialPerm([ 1, 2, 3], [ 2, 3, 1])]);;
gap> IsInverseSemigroup(S);
true
gap> JoinIrreducibleDClasses(S) = DClasses(S);
true
gap> ForAll(DClassReps(S), x -> IsJoinIrreducible(S, x));
true
# attrinv: JoinIrreducibleDClasses, partial perms, 4
gap> S := Semigroup([
> PartialPerm([ 1, 2, 3, 4, 5, 7, 6]),
> PartialPerm([ 2, 1]),
> PartialPerm([ 4, 5], [ 5, 4])]);;
gap> D := JoinIrreducibleDClasses(S);;
gap> reps := Filtered(DClassReps(S), x -> x <> MultiplicativeZero(S));;
gap> Length(D) = Length(reps);
true
gap> Length(D);
3
gap> ForAll(reps, x -> ForAny(D, d -> x in d));
true
# attrinv: JoinIrreducibleDClasses, inverse op, 1/?
gap> S := InverseMonoid([Bipartition([[ 1, 2, 5, - 2, - 3, - 5], [ 3, 4, - 1, - 4]]),
> Bipartition([[ 1, 4, - 5], [ 2, 5, - 1, - 2, - 3], [ 3, - 4]])]);;
gap> jid :=
> [DClass(S, Bipartition([[ 1, 4, - 1, - 4], [ 2, 3, 5, - 2, - 3, - 5]])),
> DClass(S, Bipartition([[ 1, 2, 3, - 1, - 2, - 3], [ 4, - 4], [ 5, - 5]]))];;
gap> JoinIrreducibleDClasses(S) = jid or JoinIrreducibleDClasses(S) = Set(jid);
true
# attrinv: MajorantClosure, 1/ 1
gap> S := DualSymmetricInverseMonoid( 3);
<inverse block bijection monoid of degree 3 with 3 generators>
gap> Size(S);
25
gap> T := InverseMonoid([Bipartition([[ 1, - 1], [ 2, 3, - 2, - 3]]),
> Bipartition([[ 1, - 2], [ 2, 3, - 1, - 3]])]);
<inverse block bijection monoid of degree 3 with 2 generators>
gap> MajorantClosure(S, T);
[ <block bijection: [ 1, 2, 3, - 1, - 2, - 3 ]>,
<block bijection: [ 1, 3, - 1, - 3 ], [ 2, - 2 ]>,
<block bijection: [ 1, 3, - 2, - 3 ], [ 2, - 1 ]>,
<block bijection: [ 1, - 1 ], [ 2, 3, - 2, - 3 ]>,
<block bijection: [ 1, - 2 ], [ 2, 3, - 1, - 3 ]>,
<block bijection: [ 1, - 1 ], [ 2, - 2 ], [ 3, - 3 ]>,
<block bijection: [ 1, 2, - 1, - 2 ], [ 3, - 3 ]>,
<block bijection: [ 1, 2, - 1, - 3 ], [ 3, - 2 ]>,
<block bijection: [ 1, 2, - 1 ], [ 3, - 2, - 3 ]>,
<block bijection: [ 1, 2, - 2, - 3 ], [ 3, - 1 ]>,
<block bijection: [ 1, 2, - 2 ], [ 3, - 1, - 3 ]>,
<block bijection: [ 1, 2, - 3 ], [ 3, - 1, - 2 ]>,
<block bijection: [ 1, 3, - 1, - 2 ], [ 2, - 3 ]>,
<block bijection: [ 1, 3, - 1 ], [ 2, - 2, - 3 ]>,
<block bijection: [ 1, 3, - 2 ], [ 2, - 1, - 3 ]>,
<block bijection: [ 1, 3, - 3 ], [ 2, - 1, - 2 ]>,
<block bijection: [ 1, - 1, - 2 ], [ 2, 3, - 3 ]>,
<block bijection: [ 1, - 1, - 3 ], [ 2, 3, - 2 ]>,
<block bijection: [ 1, - 2, - 3 ], [ 2, 3, - 1 ]>,
<block bijection: [ 1, - 3 ], [ 2, 3, - 1, - 2 ]>,
<block bijection: [ 1, - 1 ], [ 2, - 3 ], [ 3, - 2 ]>,
<block bijection: [ 1, - 2 ], [ 2, - 1 ], [ 3, - 3 ]>,
<block bijection: [ 1, - 3 ], [ 2, - 1 ], [ 3, - 2 ]>,
<block bijection: [ 1, - 2 ], [ 2, - 3 ], [ 3, - 1 ]>,
<block bijection: [ 1, - 3 ], [ 2, - 2 ], [ 3, - 1 ]> ]
gap> MajorantClosure(T, S);
Error, the 2nd argument (a semigroup) is not a subset of the 1st argument (an \
inverse semigroup)
gap> MajorantClosure(S, Elements(T));
[ <block bijection: [ 1, 2, 3, - 1, - 2, - 3 ]>,
<block bijection: [ 1, 3, - 1, - 3 ], [ 2, - 2 ]>,
<block bijection: [ 1, 3, - 2, - 3 ], [ 2, - 1 ]>,
<block bijection: [ 1, - 1 ], [ 2, 3, - 2, - 3 ]>,
<block bijection: [ 1, - 2 ], [ 2, 3, - 1, - 3 ]>,
<block bijection: [ 1, - 1 ], [ 2, - 2 ], [ 3, - 3 ]>,
<block bijection: [ 1, 2, - 1, - 2 ], [ 3, - 3 ]>,
<block bijection: [ 1, 2, - 1, - 3 ], [ 3, - 2 ]>,
<block bijection: [ 1, 2, - 1 ], [ 3, - 2, - 3 ]>,
<block bijection: [ 1, 2, - 2, - 3 ], [ 3, - 1 ]>,
<block bijection: [ 1, 2, - 2 ], [ 3, - 1, - 3 ]>,
<block bijection: [ 1, 2, - 3 ], [ 3, - 1, - 2 ]>,
<block bijection: [ 1, 3, - 1, - 2 ], [ 2, - 3 ]>,
<block bijection: [ 1, 3, - 1 ], [ 2, - 2, - 3 ]>,
<block bijection: [ 1, 3, - 2 ], [ 2, - 1, - 3 ]>,
<block bijection: [ 1, 3, - 3 ], [ 2, - 1, - 2 ]>,
<block bijection: [ 1, - 1, - 2 ], [ 2, 3, - 3 ]>,
<block bijection: [ 1, - 1, - 3 ], [ 2, 3, - 2 ]>,
<block bijection: [ 1, - 2, - 3 ], [ 2, 3, - 1 ]>,
<block bijection: [ 1, - 3 ], [ 2, 3, - 1, - 2 ]>,
<block bijection: [ 1, - 1 ], [ 2, - 3 ], [ 3, - 2 ]>,
<block bijection: [ 1, - 2 ], [ 2, - 1 ], [ 3, - 3 ]>,
<block bijection: [ 1, - 3 ], [ 2, - 1 ], [ 3, - 2 ]>,
<block bijection: [ 1, - 2 ], [ 2, - 3 ], [ 3, - 1 ]>,
<block bijection: [ 1, - 3 ], [ 2, - 2 ], [ 3, - 1 ]> ]
gap> MajorantClosure(S, Elements(S)) = Elements(S);
true
gap> MajorantClosure(T, Elements(S));
Error, the 2nd argument (a mult. elt. coll.) is not a subset of the 1st argume\
nt (an inverse semigroup)
gap> MajorantClosure(S, [One(S)]);
[ <block bijection: [ 1, - 1 ], [ 2, - 2 ], [ 3, - 3 ]> ]
# attrinv: RightCosetsOfInverseSemigroup, 1/ 2
gap> S := InverseMonoid([PartialPerm([ 1, 2, 3, 4], [ 2, 4, 1, 5]),
> PartialPerm([ 1, 3, 5], [ 5, 1, 3])]);;
gap> T := InverseSemigroup(
> [PartialPerm([ 3], [ 4]), PartialPerm([ 1, 3, 5], [ 3, 5, 1])]);;
gap> RightCosetsOfInverseSemigroup(S, T);
Error, the 2nd argument (an inverse semigroup) must be majorantly closed
gap> RightCosetsOfInverseSemigroup(S,
> InverseSemigroup(MajorantClosure(S, T), rec(small := true)));
[ [ <empty partial perm>, <identity partial perm on [ 1 ]>, [ 1, 2], [ 1, 3],
[ 1, 4], [ 1, 5], [ 2, 1], <identity partial perm on [ 2 ]>, [ 2, 3], [ 2, 4],
[ 2, 5], <identity partial perm on [ 1, 2 ]>, [ 2, 5]( 1), [ 1, 2, 4], [ 2, 1, 3],
[ 1, 3][ 2, 4], [ 1, 4][ 2, 5], [ 1, 5][ 2, 3], [ 3, 1], [ 3, 2],
<identity partial perm on [ 3 ]>, [ 3, 4], [ 3, 5],
<identity partial perm on [ 1, 3 ]>,
<identity partial perm on [ 1, 2, 3 ]>, [ 3, 1, 2], [ 3, 1, 2, 4], [ 1, 3, 5],
[ 1, 4][ 3, 2], [ 1, 4]( 3), [ 1, 4][ 3, 2, 5], [ 3, 1, 5], [ 1, 5][ 3, 4], [ 4, 1], [ 4, 2],
[ 4, 3], <identity partial perm on [ 4 ]>, [ 4, 5], [ 3, 1][ 4, 2], [ 3, 1][ 4, 5],
[ 3, 2]( 4), [ 4, 1]( 3), <identity partial perm on [ 3, 4 ]>, [ 3, 4, 5],
[ 4, 3, 5], [ 4, 2, 1], [ 2, 1][ 4, 5], <identity partial perm on [ 2, 4 ]>,
[ 2, 3][ 4, 1], [ 2, 3]( 4), [ 2, 4, 5], [ 2, 5][ 4, 3],
<identity partial perm on [ 1, 2, 4 ]>,
<identity partial perm on [ 1, 2, 3, 4 ]>, [ 1, 2, 4, 5], [ 3, 1, 2, 4, 5],
[ 4, 2, 1, 3], [ 5, 1], [ 5, 2], [ 5, 3], [ 5, 4], <identity partial perm on [ 5 ]>,
[ 4, 1][ 5, 2], [ 4, 1]( 5), [ 5, 4, 2], [ 4, 3][ 5, 1], [ 5, 4, 3],
<identity partial perm on [ 4, 5 ]>, [ 4, 5, 3], [ 5, 3, 1], [ 3, 2][ 5, 1],
<identity partial perm on [ 3, 5 ]>, [ 3, 4][ 5, 2], [ 5, 3, 4], [ 3, 5, 1],
[ 3, 5, 4], [ 5, 4, 2, 1], <identity partial perm on [ 2, 4, 5 ]>,
[ 4, 1][ 5, 2, 3], [ 5, 2]( 1), <identity partial perm on [ 1, 5 ]>,
<identity partial perm on [ 1, 3, 5 ]>,
<identity partial perm on [ 1, 2, 4, 5 ]>,
<identity partial perm on [ 1, 2, 3, 4, 5 ]>, [ 1, 2][ 5, 4], [ 5, 1, 3],
[ 1, 3][ 5, 4], ( 1, 3, 5), [ 5, 4, 2, 1, 3], [ 1, 4]( 5), [ 1, 5, 3], ( 1, 5, 3) ] ]
gap> T := InverseSemigroup([PartialPerm([ 1, 2, 4, 6, 8], [ 2, 10, 3, 5, 7]),
> PartialPerm([ 1, 3, 4, 5, 6, 7, 8], [ 4, 7, 6, 9, 10, 1, 3])]);;
gap> RightCosetsOfInverseSemigroup(S, T);
Error, the 2nd argument (an inverse semigroup) must be a subsemigroup of the 1\
st argument (an inverse semigroup)
# attrinv: RightCosetsOfInverseSemigroup, 2/ 2
gap> S := InverseSemigroup([
> PartialPerm([ 1, 2, 3, 4], [ 4, 1, 2, 6]),
> PartialPerm([ 1, 2, 3, 4], [ 5, 7, 1, 6]),
> PartialPerm([ 1, 2, 3, 5], [ 5, 2, 7, 3]),
> PartialPerm([ 1, 2, 3, 6, 7], [ 1, 3, 4, 7, 5]),
> PartialPerm([ 1, 2, 3, 4, 5, 7], [ 3, 2, 4, 6, 1, 5])]);;
gap> W := InverseSemigroup(MajorantClosure(S,
> [PartialPerm([ 1, 2, 3, 4], [ 1, 2, 3, 4])]));
<inverse partial perm semigroup of rank 7 with 5 generators>
gap> Set(RightCosetsOfInverseSemigroup(S, W));
[ [ <identity partial perm on [ 1, 2, 3, 4 ]>,
<identity partial perm on [ 1, 2, 3, 4, 5 ]>,
<identity partial perm on [ 1, 2, 3, 4, 6 ]>,
<identity partial perm on [ 1, 2, 3, 4, 5, 6 ]>,
<identity partial perm on [ 1, 2, 3, 4, 5, 7 ]> ], [ [ 2, 5]( 1)( 3)( 4) ],
[ [ 4, 3, 2, 7]( 1) ], [ [ 2, 1, 3, 4, 6] ],
[ [ 1, 3, 4, 6]( 2), [ 5, 1, 3, 4, 6]( 2), [ 7, 5, 1, 3, 4, 6]( 2) ], [ [ 1, 3, 5][ 4, 7]( 2) ],
[ [ 1, 3, 2, 5]( 4) ], [ [ 3, 2, 1, 4, 6] ], [ [ 3, 1, 4, 5]( 2) ],
[ [ 4, 3, 1, 5]( 2), [ 4, 3, 1, 5, 7]( 2), [ 6, 4, 3, 1, 5]( 2), [ 6, 4, 3, 1, 5, 7]( 2) ],
[ [ 1, 5][ 2, 4, 3, 6] ], [ [ 2, 7][ 4, 3, 1, 5] ], [ [ 2, 7][ 3, 1, 5][ 4, 6] ],
[ [ 4, 1, 6]( 2)( 3) ], [ [ 3, 5][ 4, 1, 7]( 2), [ 4, 1, 7][ 6, 3, 5]( 2) ], [ [ 2, 3, 4, 1, 7] ],
[ [ 3, 1, 7][ 4, 2, 6] ] ]
# attrinv: SupremumIdempotents, 1/ 1
gap> SupremumIdempotentsNC([], PartialPerm([]));
<empty partial perm>
gap> SupremumIdempotentsNC([], Bipartition([[ 1], [- 1]]));
<bipartition: [ 1 ], [ - 1 ]>
gap> SupremumIdempotentsNC([], Bipartition([[ 1, - 1]]));
<block bijection: [ 1, - 1 ]>
gap> SupremumIdempotentsNC(Idempotents(DualSymmetricInverseMonoid( 3)),
> RandomBlockBijection( 3));
<block bijection: [ 1, - 1 ], [ 2, - 2 ], [ 3, - 3 ]>
gap> SupremumIdempotentsNC(Transformation([ 1, 1]), 1);
Error, the argument is not a collection of partial perms, block bijections, or\
partial perm bipartitions
# attrinv: InversesOfSemigroupElementNC, 1/ 1
gap> S := InverseSemigroup(
> [Bipartition([[ 1, 2, 4, - 2, - 3], [ 3, - 4, - 5], [ 5, - 1]]),
> Bipartition([[ 1, 2, 3, 4, 5, - 1, - 2, - 3, - 4, - 5]]),
> Bipartition([[ 1, 2, 3, 4, - 2, - 3], [ 5, - 1, - 4, - 5]])]);;
gap> x := Bipartition([[ 1, - 3, - 5], [ 2, 3, 4, 5, - 1, - 2, - 4]]);;
gap> InversesOfSemigroupElementNC(S, x);
[ <block bijection: [ 1, 2, 4, - 2, - 3, - 4, - 5 ], [ 3, 5, - 1 ]> ]
gap> x in last;
false
# attrinv: IdempotentGeneratedSubsemigroup
gap> IdempotentGeneratedSubsemigroup(FreeInverseSemigroup( 2));
Error, no method found! For debugging hints type ?Recovery from NoMethodFound
Error, no 4th choice method found for `IdempotentGeneratedSubsemigroup' on 1 a\
rguments
gap> S := InverseSemigroup([
> PartialPerm([ 1, 2, 3, 4], [ 6, 2, 4, 3]),
> PartialPerm([ 1, 2, 3, 5], [ 5, 6, 3, 2]),
> PartialPerm([ 1, 2, 5], [ 3, 5, 4])]);;
gap> S := IdempotentGeneratedSubsemigroup(S);;
gap> HasIsIdempotentGenerated(S) and IsIdempotentGenerated(S);
true
#
gap> SEMIGROUPS.StopTest();
gap> STOP_TEST("Semigroups package: standard/attributes/inverse.tst");
[Verzeichnis aufwärts0.74unsichere VerbindungÜbersetzung europäischer Sprachen durch Browser2026-06-17]
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2026-07-27
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