Special values of Grothendieck polynomials in terms of hypergeometric functions

2024/02/12 by Taikei Fujii, Fujii, Taikei, Takahiko Nobukawa +3
Computer Science · Engineering · Mathematics · #05A15 #05A17 #05E05 #33C70 #33C80 #Advanced Numerical Analysis Techniques #Combinatorics (math.CO) #FOS: Mathematics #Iterative Methods for Nonlinear Equations #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2402.07424

openalex publication_date 2024/02/12 · openalex created_date 2024/02/14 · openalex updated_date 2026/07/28

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 ₂F₁. 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⁾.

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