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A358041
The number of maximal antichains in the lattice of set partitions of an n-element set.
1
1, 2, 3, 32, 14094
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.
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
Cf. A302250 (number of antichains in the lattice of set partitions).
Cf. A326358 (number of maximal antichains in the Boolean lattice).
Sequence in context: A371117 A277481 A079883 * A066269 A376557 A083785
KEYWORD
nonn,hard,more
AUTHOR
Dmitry I. Ignatov, Oct 29 2022
STATUS
approved