Combinatorial characterization of Schubert polynomial structure constants

Characterize the structure constants c^{\gamma}_{\alpha,\beta} in products of Schubert polynomials \mathfrak{S}_{\alpha}\mathfrak{S}_{\beta}, including a combinatorial description that determines their values for triples of permutations.

Background

Schubert polynomials are indexed by permutations and have connections to algebraic geometry, Lie theory, and representation theory. Their products expand in the Schubert basis with integer structure constants c^{\gamma}_{\alpha,\beta}. The paper presents understanding these constants as an important open problem and supplies datasets of permutation triples labeled by the corresponding coefficients.