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 structure constants involved in the product of two Grothendieck polynomials of Grassmannian type. In this paper, we provide an explicit combinatorial formula in terms of set-valued contratableau for the K-theoretic Littlewood-Richardson rule generalizing contratableau model for the classical Littlewood-Richardson rule given by Carr\'e.