OFFSET
1,1
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 includes the empty antichain consisting of no set partitions.
LINKS
Dmitry I. Ignatov, A Note on the Number of (Maximal) Antichains in the Lattice of Set Partitions. In: Ojeda-Aciego, M., Sauerwald, K., Jäschke, R. (eds) Graph-Based Representation and Reasoning. ICCS 2023. Lecture Notes in Computer Science(). Springer, Cham.
EXAMPLE
For n = 3 the a(3) = 10 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() for n in range(4)]
CROSSREFS
KEYWORD
nonn,hard,more
AUTHOR
John Machacek, Apr 04 2018
STATUS
approved