Padded Schubert polynomials and weighted enumeration of Bruhat chains

Abstract

We prove a common generalization of the fact that the weighted number of maximal chains in the strong Bruhat order on the symmetric group is $\left(\genfrac{}{}{0ex}{}{n}{2}\right)!$ for both the code weights and the Chevalley weights. We also define weights which give a one-parameter family of strong order analogues of Macdonald's reduced word identity for Schubert polynomials.

12 pages, comments welcome; v2: minor edits and journal reference. Published version appears under the title "Weighted enumeration of Bruhat chains in the symmetric group", original title has been kept here due to existing references