Enumeration of bigrassmannian permutations below a permutation in Bruhat order

Details Enumeration of bigrassmannian permutations below a permutation in Bruhat order Enumeration of bigrassmannian permutations below a permutation in Bruhat order

2010-05-18

arxiv.org/abs/1005.3335v1

Order (Published online on May 13, 2010)

Mathematics

Combinatorics

7 pages.

Scientific paper

10.1007/s11083-010-9157-1

In theory of Coxeter groups, bigrassmannian elements are well known as elements which have precisely one left descent and precisely one right descent. In this article, we prove formulas on enumeration of bigrassmannian permutations weakly below a permutation in Bruhat order in the symmetric groups. For the proof, we use equivalent characterizations of bigrassmannian permutations by Lascoux-Schutzenberger and Reading.

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