Grothendieck polynomials of inverse fireworks permutations

Abstract

Pipedreams are combinatorial objects that compute Grothendieck polynomials. We introduce a new combinatorial object that naturally recast the pipedream 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 M\'esz\'aros, Setiabrata, and St. Dizier on the support of Grothendieck polynomials.