Cancellation-free SEM expansion formula

Derive a cancellation-free formula for the expansion of an arbitrary Schubert polynomial into standard elementary monomials.

Background

The paper studies expansions of Schubert polynomials in the basis of standard elementary monomials (SEMs), emphasizing their relevance to quantum Schubert polynomials. Although determinantal formulas and results for restricted pattern classes are known, the authors state that a cancellation-free formula for general SEM expansions is not known.

References

Despite this progress, SEM expansions for Schubert polynomials more generally are far from well understood: giving a cancellation-free formula for the expansion of a Schubert polynomial into SEMs remains an open problem, and many other properties of these expansions remain mysterious.

— Single-SEM Schubert Polynomials  (2503.03903 - Woodruff, 5 Mar 2025) in Introduction