cp's OEIS Frontend

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.

%I A215651 #25 Mar 25 2021 10:19:36
%S A215651 1,2,8,283,132069776
%N 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.
%C A215651 The semigroup analog of A000638.
%C A215651 We apply the categorical viewpoint and consider the empty set as a semigroup.
%H A215651 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 A215651 (GAP)
%o A215651 ################################################################################
%o A215651 # GAP 4.5 function calculating the conjugacy classes of a set of subsemigrops.
%o A215651 # (C) 2012 Attila Egri-Nagy www.egri-nagy.hu
%o A215651 # GAP can be obtained from www.gap-system.org
%o A215651 ################################################################################
%o A215651 # Input: list of subsemigroups of a transformation semigroup,
%o A215651 #        automorphism group of the semigroup
%o A215651 # Output: list of conjugacy classes
%o A215651 ConjugacyClassesSubsemigroups := function(subsemigroups, G)
%o A215651 local ssg, #subsemigroup
%o A215651       ccl, #conjugacy class
%o A215651       ccls; #result: all conjugacy classes
%o A215651   ccls := [];
%o A215651   for ssg in subsemigroups do
%o A215651     #we check whether the subsemigroup is already in a conjugacy class
%o A215651     if not ForAny(ccls, x -> ssg in x) then
%o A215651       #conjugating by all group elements
%o A215651       ccl := DuplicateFreeList(
%o A215651                      List(G,
%o A215651                           g -> AsSortedList(List(ssg, t-> t^g))));
%o A215651       Add(ccls, ccl);
%o A215651     fi;
%o A215651   od;
%o A215651   return ccls;
%o A215651 end;
%Y A215651 Cf. A000638, A215650.
%K A215651 nonn,more
%O A215651 0,2
%A A215651 _Attila Egri-Nagy_, Aug 19 2012
%E A215651 a(4) moved from a comment by _Attila Egri-Nagy_, Jan 09 2014 to data by _Andrey Zabolotskiy_, Mar 25 2021