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) 869-921.
J. D. Mitchell et al., Semigroups package for GAP.
PROG
(GAP) for i in [2 .. 8] do
Print(NrIdempotents(PartitionMonoid(i)), "\n");
od;
CROSSREFS
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