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A215651 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. 1

%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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Last modified March 5 02:31 EST 2024. Contains 370537 sequences. (Running on oeis4.)