Deciding Vanishing of Schubert Polynomial Coefficients

The Schubitope \(S_w\) is the convex hull of exponent vectors appearing in the Schubert polynomial associated to the permutation \(w\). All integral points in the Schubitope appear as the exponent vector of some term in the associated polynomial. We discuss a polynomial time algorithm, discovered by Adve, Robichaux, and Yong, for deciding if a given exponent vector is in the Schubitope of a given permutation. The proof relies on a tableau criterion that reduces to a tractable linear programming problem.

Date published: Wednesday, February 22, 2023