A tableau formula of double Grothendieck polynomials for $321$-avoiding permutations

TL;DR

This paper establishes a tableau formula for double Grothendieck polynomials linked to 321-avoiding permutations, enhancing understanding of their combinatorial structure within algebraic geometry.

Contribution

It introduces a new tableau formula for these polynomials and demonstrates its compatibility with K-theoretic divided difference operators.

Findings

The tableau formula accurately represents double Grothendieck polynomials for 321-avoiding permutations.

The formula is compatible with K-theoretic divided difference operators.

Provides a combinatorial tool for studying these polynomials.

Abstract

In this article, we prove a tableau formula for the double Grothendieck polynomials associated to $321$-avoiding permutations. The proof is based on the compatibility of the formula with the $K$-theoretic divided difference operators.