|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
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
|
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
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|