Counterexamples to Robichaux's conjecture for Grothendieck polynomials

Abstract

Ross and Yong conjectured a $K$-theoretic Kohnert rule for Grothendieck polynomials. Robichaux exhibited a counterexample to the Ross--Yong rule and proposed a revised ghost $K$-Kohnert rule, proving both rules hold for 321-avoiding permutations. We provide counterexamples to Robichaux's rule and give an explicit bijection showing that both the Ross--Yong and Robichaux rules hold for 1432-avoiding permutations. As an application, we provide a Kohnert-theoretic characterization of 1432-avoidance.