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arXiv · 2202.02897

Proof of a conjectured Möbius inversion formula for Grothendieck polynomials

Oliver Pechenik·Matthew Satriano
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Abstract

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

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Oliver Pechenik, Matthew Satriano. 2022-02-21. Proof of a conjectured Möbius inversion formula for Grothendieck polynomials. https://arxiv.org/abs/2202.02897

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