Year: 2026
Type: preprint
Abstract: We prove that monomial coefficients in affine families of key and Schubert polynomials are eventually polynomial. These results extend to finite products. Using M.~Watanabe's Schubert duality, we deduce that stretched Schubert structure constants are eventually polynomial. This proves a conjecture stated by I.~Pak and Z.~Slonim. We also prove that the positive key expansion of every affine-code family of Schubert polynomials eventually has fixed coefficients and affine indices. The proofs combine Demazure operators and vector partition functions with P.~Magyar's orthodontic formula and the generalized Demazure character theory of V.~Lakshmibai, P.~Littelmann, and P.~Magyar.
Source: arXiv (Cornell University)
Author: Alexandersson, Per
Institution: Stockholm University
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7170063717