2021/06/26 by Mark Shimozono, Tianyi Yu, Shimozono, Mark +1
Mathematics · #05E14 14N15 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2106.13922
openalex publication_date 2021/06/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We establish the conjecture of Reiner and Yong for an explicit combinatorial formula for the expansion of a Grothendieck polynomial into the basis of Lascoux polynomials. This expansion is a subtle refinement of its symmetric function version due to Buch, Kresch, Shimozono, Tamvakis, and Yong, which gives the expansion of stable Grothendieck polynomials indexed by permutations into Grassmannian stable Grothendieck polynomials. Our expansion is the K-theoretic analogue of that of a Schubert polynomial into Demazure characters, whose symmetric analogue is the expansion of a Stanley symmetric function into Schur functions. Our expansions extend to flagged Grothendieck polynomials.