Problems / combinatorics

combinatorics / Algebraic combinatorics

Pak-Slonim Conjecture on Stretched Schubert Structure Constants

Pak and Slonim conjectured that stretched Schubert structure constants are eventually polynomial. They are. Monomial coefficients in affine families of key and Schubert polynomials are eventually polynomial, and the Schubert duality of Watanabe carries this to the structure constants. The same result settles the polynomiality half of a conjecture of Alexandersson and Alhajjar for key polynomials.