A Contratableau Model for K-theoretic Littlewood–Richardson Rule

Abstract

The K-theoretic Littlewood–Richardson rule, established by A. Buch, is a combinatorial method for counting the coefficients in the expansion of the product of two symmetric Grothendieck polynomials as a linear combination of symmetric Grothendieck polynomials. In this paper, we provide an explicit combinatorial formula in terms of set-valued contratableaux for the K-theoretic Littlewood--Richardson rule, generalizing the contratableau model for the classical Littlewood--Richardson rule introduced by Carré.