A384687 - OEIS

A384687

Number of elements in the Dedekind-MacNeille completion of the Bruhat order on D_n.

4, 42, 1292, 114976, 29735760

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OFFSET

2,1

COMMENTS

This sequence is the number of elements in the Dedekind-MacNeille completion (completion by cuts) of the Bruhat order of the Weyl group D_n. It is a type D analog of A378072.

LINKS

Table of n, a(n) for n=2..6.

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

EXAMPLE

For n=2 the Bruhat order on D_2 consists of four elements, 1 (identity), s1, s2, and s2*s1. Its completion forms the diamond lattice and coincides with the order.

s2*s1

/ \

s1 s2

\ /

CROSSREFS

Cf. A002866 (group D_n order), A005130 (completion for A_n), A378072 (completion for B_n).

Sequence in context: A156479 A355130 A355124 * A111829 A200000 A198209

Adjacent sequences: A384684 A384685 A384686 * A384688 A384689 A384690

KEYWORD

nonn,more

AUTHOR

Dmitry I. Ignatov, Jun 07 2025

STATUS

approved