A382350 Number of maximal antichains in the Bruhat order on B_n.
2, 5, 215, 24828398365
Offset: 1
Examples
For n=1 the elements are 1 (identity) and s1, the order contains pair (1, s1). The maximal antichains are {1} and {s1}.
For n=2 the line (Hasse) diagram is below.
s2*s1*s2*s1
/ \
s2*s1*s2 s1*s2*s1
| X |
s2*s1 s1*s2
| X |
s2 s1
\ /
1
The set of maximal antichains is {{1}, {s2, s1}, {s2*s1, s1*s2}, {s2*s1*s2, s1*s2*s1}, {s2*s1*s2*s1}}.
References
- A. Bjorner and F. Brenti, Combinatorics of Coxeter Groups, Springer, 2009, 27-64.
Links
- V. V. Deodhar, On Bruhat ordering and weight-lattice ordering for a Weyl group, Indagationes Mathematicae, vol. 81, 1 (1978), 423-435.
Crossrefs
Extensions
a(4) from Dmitry I. Ignatov, Aug 15 2025
Comments