A378072 Number of elements in the completion of the Bruhat order on B_n.

1, 2, 10, 132, 4824, 493600, 142343254

Offset: 0

Author

Ludovic Schwob, Nov 16 2024

Keywords

• nonn
• more

Comments

Lascoux and Schützenberger have shown that the completion of type B Bruhat order is distributive, and have described its irreducible elements. It follows that a(n) is the number of antichains in the poset of irreducible elements of the Bruhat order on B_n.

This sequence is a type B analog of A005130, since ASMs form a lattice isomorphic to the completion of type A Bruhat order.

Links

• A. Lascoux and M.-P. Schützenberger, Treillis et bases des groupes de Coxeter, Electron. J. Combin. 3 (1996), #R27.

Crossrefs

Cf. A005130 (ASMs), A005158 (centrally symmetric ASMs), A000165 (number of elements in B_n).

Extensions

a(6) by Dmitry I. Ignatov, May 16 2025