Proof of a conjectured Möbius inversion formula for Grothendieck polynomials

2022/02/07 by Oliver Pechenik, Matthew Satriano, Pechenik, Oliver +1
Mathematics · Pharmacology, Toxicology and Pharmaceutics · #05E05 #14M15 #14N15 #Advanced Combinatorial Mathematics #Algebraic Geometry and Number Theory #Alkaloids: synthesis and pharmacology #Combinatorics (math.CO) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2202.02897

openalex publication_date 2022/02/07 · openalex created_date 2022/04/03 · openalex updated_date 2026/07/28

Abstract

Schubert polynomials \mathfrakS_w are polynomial representatives for cohomology classes of Schubert varieties in a complete flag variety, while Grothendieck polynomials \mathfrakG_w are analogous representatives for the K-theory classes of the structure sheaves of Schubert varieties. In the special case that \mathfrakS_w is a multiplicity-free sum of monomials, K. Mészáros, L. Setiabrata, and A. St. Dizier conjectured that \mathfrakG_w can be easily computed from \mathfrakS_w via Möbius inversion on a certain poset. We prove this conjecture.

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