Marked Bumpless Pipedreams and Compatible Pairs

TL;DR

This paper introduces a bijection linking marked bumpless pipedreams with reverse compatible pairs to not-necessarily-reduced pipedreams, unifying multiple formulas for Grothendieck polynomials and generalizing previous bijections.

Contribution

It presents a new bijection that unifies various formulas for Grothendieck polynomials and generalizes earlier bijections to the marked, non-reduced case.

Findings

Unified formulas for Grothendieck polynomials

Bijection between marked bumpless pipedreams and not-necessarily-reduced pipedreams

Generalization of Gao and Huang's bijection

Abstract

We construct a bijection between marked bumpless pipedreams with reverse compatible pairs, which are in bijection with not-necessarily-reduced pipedreams. This directly unifies various formulas for Grothendieck polynomials in the literature. Our bijection is a generalization of a variant of the bijection of Gao and Huang in the unmarked, reduced case.