A384959 Number of chains in the Bruhat order of type A_n.

4, 36, 4524, 15166380, 2010484649524, 14206021962108887860

Offset: 1

Author

Dmitry I. Ignatov, Jun 13 2025

Keywords

• nonn
• more

Comments

The number of chains in the Bruhat order of the Weyl group A_n (isomorphic to the symmetric group S_{n+1}).

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.
• A. Postnikov and R. P. Stanley, Chains in the Bruhat order, J. Algebr. Comb., 29 (2009), 133-174.

Crossrefs

Cf. A061710 (maximal chains), A000142 (the order size), A005130 (the size of Dedekind-MacNeille completion), A384061 (number of antichains).