OFFSET
1,2
COMMENTS
Also similar to the number of maximal antichains in the Boolean lattice.
LINKS
R. L. Graham, Maximum antichains in the partition lattice, The Mathematical Intelligencer, 1 (1978), 84-86.
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.
Dmitry I. Ignatov, Supporting iPython code and input files for counting (maximal) antichains of the set partition lattice up to n=5, Github repository.
EXAMPLE
For n = 3 the a(3) = 3 maximal antichains are: {1|2|3}, {1|23, 12|3, 13|2}, and {123}. We use the typical shorthand notation for set partitions where 1|23 denotes {{1}, {2,3}}.
CROSSREFS
KEYWORD
nonn,hard,more
AUTHOR
Dmitry I. Ignatov, Oct 29 2022
STATUS
approved