| Quellcodebibliothek Statistik Leitseite products/Sources/formale Sprachen/GAP/pkg/semigroups/tst/standard/attributes/ (GAP Algebra Version 4.15.1©) Datei vom 29.7.2025 mit Größe 78 kB |
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Impressum inverse.tst Sprache: unbekannt |
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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"); [Seitenstruktur0.119Druckenetwas mehr zur Ethik2026-06-17] |
2026-07-27