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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
1, 2, 8, 283, 132069776
OFFSET
0,2
COMMENTS
The semigroup analog of A000638.
We apply the categorical viewpoint and consider the empty set as a semigroup.
LINKS
James East, Attila Egri-Nagy, James D. Mitchell, Enumerating Transformation Semigroups, Semigroup Forum 95, 109-125 (2017); arXiv: 1403.0274 [math.GR], 2014-2017.
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
Sequence in context: A009675 A012301 A296406 * A363180 A285850 A009501
KEYWORD
nonn,more
AUTHOR
Attila Egri-Nagy, Aug 19 2012
EXTENSIONS
a(4) moved from a comment by Attila Egri-Nagy, Jan 09 2014 to data by Andrey Zabolotskiy, Mar 25 2021
STATUS
approved