The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 (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. LINKS Table of n, a(n) for n=0..4. 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 Cf. A000638, A215650. Sequence in context: A009675 A012301 A296406 * A363180 A285850 A009501 Adjacent sequences: A215648 A215649 A215650 * A215652 A215653 A215654 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified November 29 07:51 EST 2023. Contains 367429 sequences. (Running on oeis4.)