Generalized permutahedra and Schubert calculus

TL;DR

This paper links generalized permutahedra with Schubert calculus, providing polynomial-time criteria for vanishing Schubert intersection numbers using Schubitopes, advancing computational methods in algebraic geometry.

Contribution

It introduces a novel connection between generalized permutahedra and Schubert calculus, offering efficient vanishing criteria via Schubitopes.

Findings

Provided polynomial-time tableau test for vanishing intersection numbers

Established sufficient vanishing criteria for Schubert intersection numbers

Connected Newton polytopes of Schubert polynomials with generalized permutahedra

Abstract

We connect generalized permutahedra with Schubert calculus. Thereby, we give sufficient vanishing criteria for Schubert intersection numbers of the flag variety. Our argument utilizes recent developments in the study of Schubitopes, which are Newton polytopes of Schubert polynomials. The resulting tableau test executes in polynomial time.