| Quellcodebibliothek Statistik Leitseite products/Sources/formale Sprachen/GAP/pkg/semigroups/tst/standard/attributes/ (Algebra von RWTH Aachen Version 4.15.1©) Datei vom 29.7.2025 mit Größe 78 kB |
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Quelle inverse.tst Sprache: unbekannt |
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## #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])]);; --> -------------------- --> maximum size reached --> -------------------- [ Dauer der Verarbeitung: 0.7 Sekunden (vorverarbeitet) ] |
2026-04-02