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

1, 2, 10, 132, 4824, 493600

Offset

0,2

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

Table of n, a(n) for n=0..5.

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).

Sequence in context: A254431 A011838 A355463 * A336537 A118183 A134051

Adjacent sequences: A378069 A378070 A378071 * A378073 A378074 A378075

Keyword

nonn,more

Author

Ludovic Schwob, Nov 16 2024

Status

approved