Abstract
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-Schützenberger and Reading.
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Kobayashi, M. Enumeration of Bigrassmannian Permutations Below a Permutation in Bruhat Order. Order 28, 131–137 (2011). https://doi.org/10.1007/s11083-010-9157-1
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DOI: https://doi.org/10.1007/s11083-010-9157-1