OFFSET
1,2
COMMENTS
Computing terms in this sequence is analogous to Dedekind's problem which asks for the number of antichains in the Boolean algebra.
This count excludes the empty antichain consisting of no set partitions.
LINKS
Sebastian Bozlee, Bob Kuo, and Adrian Neff, A classification of modular compactifications of the space of pointed elliptic curves by Gorenstein curves, arXiv:2105.10582 [math.AG], 2021.
EXAMPLE
For n = 3 the a(3) = 9 nonempty antichains are:
{1/2/3}
{1/23}
{12/3}
{13/2}
{1/23, 12/3}
{1/23, 13/2}
{12/3, 13/2}
{1/23, 12/3, 13/2}
{123}
Here we have used the usual shorthand notation for set partitions where 1/23 denotes {{1}, {2,3}}.
PROG
(Sage)
[Posets.SetPartitions(n).antichains().cardinality() - 1 for n in range(4)]
# minus removes the empty antichain
CROSSREFS
KEYWORD
nonn,hard,more
AUTHOR
John Machacek, Apr 04 2018
STATUS
approved