Weighted enumeration of Bruhat chains in the symmetric group

Weighted enumeration of Bruhat chains in the symmetric group

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 (n2)!{n \choose 2}! for both the code weights and the Chevalley weights, generalizing a result of St...

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Veröffentlicht in:Proceedings of the American Mathematical Society 2020-09, Vol.148 (9), p.3749-3759
Hauptverfasser: Gaetz, Christian, Gao, Yibo
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description 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 (n2)!{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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title Weighted enumeration of Bruhat chains in the symmetric group
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