A358391 The number of antichains in the Kreweras lattice of non-crossing set partitions of an n-element set.

2, 3, 10, 234, 2342196

Offset: 1

Author

Dmitry I. Ignatov, Nov 13 2022

Keywords

• nonn
• hard
• more

Comments

This is also the number of order ideals (down-sets) for this lattice.

Also similar to the number of antichains in the lattice of set partitions or in the Boolean lattice.

Links

• Dmitry I. Ignatov, Supporting iPython code and input files for counting (maximal) antichains of the non-crossing set partition lattice up to n=5, Github repository.
• G. Kreweras, Sur les partitions non croisées d'un cycle, Discrete Math., 4(1972), 333-350.

Crossrefs

Cf. A000372 (number of antichains in the Boolean lattice).

Cf. A143673 (number of antichains in the lattice of Dyck paths).

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