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%I #25 Mar 25 2021 10:19:36
%S 1,2,8,283,132069776
%N Number of transformation semigroups acting on n points (counting conjugates as one), i.e., the number of subsemigroups of the full transformation semigroup T_n.
%C The semigroup analog of A000638.
%C We apply the categorical viewpoint and consider the empty set as a semigroup.
%H James East, Attila Egri-Nagy, James D. Mitchell, <a href="https://doi.org/10.1007/s00233-017-9869-2">Enumerating Transformation Semigroups</a>, Semigroup Forum 95, 109-125 (2017); arXiv: <a href="https://arxiv.org/abs/1403.0274">1403.0274</a> [math.GR], 2014-2017.
%o (GAP)
%o ################################################################################
%o # GAP 4.5 function calculating the conjugacy classes of a set of subsemigrops.
%o # (C) 2012 Attila Egri-Nagy www.egri-nagy.hu
%o # GAP can be obtained from www.gap-system.org
%o ################################################################################
%o # Input: list of subsemigroups of a transformation semigroup,
%o # automorphism group of the semigroup
%o # Output: list of conjugacy classes
%o ConjugacyClassesSubsemigroups := function(subsemigroups, G)
%o local ssg, #subsemigroup
%o ccl, #conjugacy class
%o ccls; #result: all conjugacy classes
%o ccls := [];
%o for ssg in subsemigroups do
%o #we check whether the subsemigroup is already in a conjugacy class
%o if not ForAny(ccls, x -> ssg in x) then
%o #conjugating by all group elements
%o ccl := DuplicateFreeList(
%o List(G,
%o g -> AsSortedList(List(ssg, t-> t^g))));
%o Add(ccls, ccl);
%o fi;
%o od;
%o return ccls;
%o end;
%Y Cf. A000638, A215650.
%K nonn,more
%O 0,2
%A _Attila Egri-Nagy_, Aug 19 2012
%E a(4) moved from a comment by _Attila Egri-Nagy_, Jan 09 2014 to data by _Andrey Zabolotskiy_, Mar 25 2021
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