Positivity of Schubert Coefficients

TL;DR

This paper introduces a positive rule for determining the positivity of Schubert coefficients, a key open problem in algebraic combinatorics, under two standard assumptions.

Contribution

It provides a new positive rule for deciding the positivity of Schubert coefficients based on two standard assumptions, advancing understanding in algebraic combinatorics.

Findings

Established a positive rule for Schubert coefficient positivity

Relied on two standard assumptions for the rule

Advances the solution to a major open problem

Abstract

Schubert coefficients $c_{u,v}^w$ are structure constants describing multiplication of Schubert polynomials. Deciding positivity of Schubert coefficients is a major open problem in Algebraic Combinatorics. We prove a positive rule for this problem based on two standard assumptions.