A358041 The number of maximal antichains in the lattice of set partitions of an n-element set.

1, 2, 3, 32, 14094

Offset: 1

Author

Dmitry I. Ignatov, Oct 29 2022

Keywords

• nonn
• hard
• more

Comments

Also similar to the number of maximal antichains in the Boolean lattice.

Examples

			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}}.
		

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.

Crossrefs

Cf. A302250 (number of antichains in the lattice of set partitions).

Cf. A326358 (number of maximal antichains in the Boolean lattice).