Special values of Grothendieck polynomials in terms of hypergeometric functions

Abstract

We give some special values of Grothendieck polynomials and an explicit formula for the number of set-valued tableaux. For Young diagrams consisting of a single row or a single column, both the value and number are written by the Gauss' hypergeometric function ${}_2F_1$. For general Young diagrams, the Holman hypergeometric function $F^{(n)}$ is used to represent both the value and count. As an application, we derive a summation formula for $F^{(n)}$.