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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2402.07424 |
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| _version_ | 1866916122001932288 |
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| author | Fujii, Taikei Nobukawa, Takahiko Shimazaki, Tatsushi |
| author_facet | Fujii, Taikei Nobukawa, Takahiko Shimazaki, Tatsushi |
| contents | 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 $F^{(n)}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_07424 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Special values of Grothendieck polynomials in terms of hypergeometric functions Fujii, Taikei Nobukawa, Takahiko Shimazaki, Tatsushi Combinatorics 05A15, 05A17, 05E05, 33C70, 33C80 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 $F^{(n)}$. |
| title | Special values of Grothendieck polynomials in terms of hypergeometric functions |
| topic | Combinatorics 05A15, 05A17, 05E05, 33C70, 33C80 |
| url | https://arxiv.org/abs/2402.07424 |