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Presented By: Department of Mathematics

Combinatorics Seminar

Bumpless pipe dreams and coefficients of Schubert polynomials

In their work on back-stable Schubert calculus, Lam, Lee, and Shimozono gave combinatorial formulas which realize the back-stable Schubert polynomials as weighted enumerators of "bumpless pipe dreams". I will describe variants of these polynomials, called "enriched Schubert polynomials", which collect the symmetric part into Schur functions. In this (re-)formulation, one can ask for the coefficient of a given Schur function in such an enriched Schubert polynomial. Answering this question leads to new bumpless pipe dream formulas, along with other combinatorial identities.

This is joint work with William Fulton. Speaker(s): David Anderson (Ohio State University)

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