A384687 Number of elements in the Dedekind-MacNeille completion of the Bruhat order on D_n.

4, 42, 1292, 114976, 29735760

Offset: 2

Author

Dmitry I. Ignatov, Jun 07 2025

Keywords

• nonn
• more

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.

Examples

			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
   \ /
    1
		

Links

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

Crossrefs

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