An efficient algorithm for deciding vanishing of Schubert polynomial coefficients
Abstract
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.
Cite
@article{arxiv.2103.05195,
title = {An efficient algorithm for deciding vanishing of Schubert polynomial coefficients},
author = {Anshul Adve and Colleen Robichaux and Alexander Yong},
journal= {arXiv preprint arXiv:2103.05195},
year = {2021}
}
Comments
30 pages. This paper was split off from 1810.10361v1, with a new title and abstract. That earlier preprint has been replaced by a conference proceedings version 1810.10361v2, with a different title and abstract; it contains complexity discussion and a related conjecture not found here. To appear in Advances in Math