Efficient computation of Schubert structure constants

Develop an algorithm that computes Schubert structure constants for the cohomology ring of the complete flag variety with substantially improved efficiency, particularly for large n, while avoiding the computational difficulties of existing polynomial-arithmetic and linear-algebra methods.

Background

Schubert structure constants determine the multiplication rules in the cohomology or Chow ring of the complete flag variety and can be computed by expanding products of Schubert polynomials. The paper explains that current methods become impractical for large n because both time and memory requirements grow rapidly. It explicitly identifies finding the most efficient possible algorithm as unresolved and connects the issue to the search for combinatorial rules generalizing Littlewood–Richardson rules.