An orthodontia formula for Grothendieck polynomials

Mészáros, Karola; Setiabrata, Linus; St. Dizier, Avery

doi:10.1090/tran/8529

An orthodontia formula for Grothendieck polynomials
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by Karola Mészáros, Linus Setiabrata and Avery St. Dizier PDF

Trans. Amer. Math. Soc. 375 (2022), 1281-1303

Abstract:

We give a new operator formula for Grothendieck polynomials that generalizes Magyar’s Demazure operator formula for Schubert polynomials. Our proofs are purely combinatorial, contrasting with the geometric and representation theoretic tools used by Magyar. We apply our formula to prove a necessary divisibility condition for a monomial to appear in a given Grothendieck polynomial.

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