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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. 0
 1, 2, 8, 283 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS The semigroup analog of A000638. We apply the categorical viewpoint and consider the empty set as a semigroup. The fifth term has been calculated: 132069776. Currently, the result is being verified and the related publication is being prepared. - Attila Egri-Nagy, Jan 09 2014 LINKS PROG (GAP) ################################################################################ # GAP 4.5 function calculating the conjugacy classes of a set of subsemigrops. # (C) 2012 Attila Egri-Nagy www.egri-nagy.hu # GAP can be obtained from www.gap-system.org ################################################################################ # Input: list of subsemigroups of a transformation semigroup, #        automorphism group of the semigroup # Output: list of conjugacy classes ConjugacyClassesSubsemigroups := function(subsemigroups, G) local ssg, #subsemigroup       ccl, #conjugacy class       ccls; #result: all conjugacy classes   ccls := [];   for ssg in subsemigroups do     #we check whether the subsemigroup is already in a conjugacy class     if not ForAny(ccls, x -> ssg in x) then       #conjugating by all group elements       ccl := DuplicateFreeList(                      List(G,                           g -> AsSortedList(List(ssg, t-> t^g))));       Add(ccls, ccl);     fi;   od;   return ccls; end; CROSSREFS Cf. A215650. Sequence in context: A012296 A009675 A012301 * A285850 A009501 A013027 Adjacent sequences:  A215648 A215649 A215650 * A215652 A215653 A215654 KEYWORD nonn,more AUTHOR Attila Egri-Nagy, Aug 19 2012 STATUS approved

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