Weighted enumeration of Bruhat chains in the symmetric group

Gaetz, Christian; Gao, Yibo

doi:10.1090/proc/15005

Weighted enumeration of Bruhat chains in the symmetric group
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by Christian Gaetz and Yibo Gao PDF

Proc. Amer. Math. Soc. 148 (2020), 3749-3759 Request permission

Abstract:

We use the recently introduced padded Schubert polynomials to prove a common generalization of the fact that the weighted number of maximal chains in the strong Bruhat order on the symmetric group is ${n \choose 2}!$ for both the code weights and the Chevalley weights, generalizing a result of Stembridge. We also define weights which give a one-parameter family of strong order analogues of Macdonald’s well-known reduced word identity for Schubert polynomials.

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