Algebraic Combinatorics Seminar - Colleen Robichaux

Thursday, March 25, 2021 1:00 pm - 1:00 pm EDT (GMT -04:00)

Title: An Efficient Algorithm for Deciding the Vanishing of Schubert Polynomial Coefficients

Speaker: Colleen Robichaux
Affiliation: University of Illinois at Urbana-Champaign
Zoom: Contact Karen Yeats


 Schubert polynomials form a basis of all polynomials and appear in the study of cohomology rings of flag manifolds. The vanishing problem for Schubert polynomials asks if a coefficient of a Schubert polynomial is zero. We give a tableau criterion to solve this problem, from which we deduce the first polynomial time algorithm. These results are obtained from new characterizations of the Schubitope, a generalization of the permutahedron defined for any subset of the n x n grid. In contrast, we show that computing these coefficients explicitly is #P-complete. This is joint work with Anshul Adve and Alexander Yong.