Grothendieck polynomials of inverse fireworks permutations

Abstract

Pipe dreams are combinatorial objects that compute Grothendieck polynomials. We introduce a new combinatorial object that naturally recasts the pipe dream formula. From this, we obtain the first direct combinatorial formula for the top degree components of Grothendieck polynomials, also known as the Castelnuovo–Mumford polynomials. We also prove the inverse fireworks case of a conjecture of Mészáros, Setiabrata, and St. Dizier on the support of Grothendieck polynomials.