Marked Bumpless Pipedreams and Compatible Pairs
Daoji Huang, Mark Shimozono, Tianyi Yu

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.
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