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arXiv · 2402.07424

Special values of Grothendieck polynomials in terms of hypergeometric functions

Taikei Fujii·Takahiko Nobukawa·Tatsushi Shimazaki
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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 $F^{(n)}$.

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Taikei Fujii, Takahiko Nobukawa, Tatsushi Shimazaki. 2024-02-12. Special values of Grothendieck polynomials in terms of hypergeometric functions. https://arxiv.org/abs/2402.07424

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