

A225797


The number of idempotents in the partition monoid on [1..n].


5



2, 12, 114, 1512, 25826, 541254, 13479500, 389855014, 12870896154, 478623817564, 19835696733562, 908279560428462, 45625913238986060, 2499342642591607902, 148545280714724993650, 9537237096314268691724
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OFFSET

1,1


COMMENTS

The partition monoid is the set of partitions on [1..2n] and multiplication as defined in Halverson and Ram.
No general formula is known for the number of idempotents in the partition monoid.
a(2) to a(8) were first produced using the Semigroups package for GAP, which contains code based on earlier calculations by Max Neunhoeffer.


LINKS

James Mitchell, Table of n, a(n) for n = 1..115
I. Dolinka, J. East, A. Evangelou, D. FitzGerald, N. Ham, et al., Enumeration of idempotents in diagram semigroups and algebras, arXiv preprint arXiv:1408.2021 [math.GR], 2014.
T. Halverson, A. Ram, Partition algebras, European J. Combin. 26 (6) (2005) 869921.
J. D. Mitchell et al., Semigroups package for GAP.


PROG

(GAP) for i in [2 .. 8] do
Print(NrIdempotents(PartitionMonoid(i)), "\n");
od;


CROSSREFS

Cf. A227545.
Sequence in context: A052696 A107723 A258175 * A302286 A035051 A214222
Adjacent sequences: A225794 A225795 A225796 * A225798 A225799 A225800


KEYWORD

nonn


AUTHOR

James Mitchell, Jul 27 2013


EXTENSIONS

a(9)a(12) from James East, Feb 07 2014
a(13) onwards from James Mitchell, May 23 2016


STATUS

approved



