Combinatorial interpretation of Schubert structure constants

Find a combinatorial interpretation of Schubert structure constants as counts of explicitly describable combinatorial objects, such as paths in Bruhat order, Mondrian tableaux, labeled diagrams, permutation arrays, or n-dimensional chess games.

Background

The structure constants are already known geometrically as numbers of points in generic zero-dimensional intersections of Schubert varieties. However, the paper emphasizes that testing genericity and solving the resulting polynomial systems are computationally difficult. A direct combinatorial rule would provide a way to calculate these constants without relying on genericity tests or high-dimensional equation solving.