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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.08041 |
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| _version_ | 1866918508655280128 |
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| author | Huang, Zihao Jiang, Wenlong Zhou, Yue |
| author_facet | Huang, Zihao Jiang, Wenlong Zhou, Yue |
| contents | In 2000, Kadell gave an orthogonality conjecture for a symmetric function generalization of the Zeilberger--Bressoud $q$-Dyson constant term identity. The non-zero part of Kadell's conjecture is a constant term identity indexed by a weak composition $v$. This conjecture was first proved by Károlyi, Lascoux and Warnaar in 2015. They further formulated a closed-form expression for the above constant term when all parts of the composition $v$ are distinct. In 2021, Zhou obtained a recursion for this constant term for an arbitrary composition $v$. In this paper, by categorizing the variables into two parts, we generalize Zhou's result. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_08041 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A generalization of Kadell's orthogonality ex-conjecture Huang, Zihao Jiang, Wenlong Zhou, Yue Combinatorics In 2000, Kadell gave an orthogonality conjecture for a symmetric function generalization of the Zeilberger--Bressoud $q$-Dyson constant term identity. The non-zero part of Kadell's conjecture is a constant term identity indexed by a weak composition $v$. This conjecture was first proved by Károlyi, Lascoux and Warnaar in 2015. They further formulated a closed-form expression for the above constant term when all parts of the composition $v$ are distinct. In 2021, Zhou obtained a recursion for this constant term for an arbitrary composition $v$. In this paper, by categorizing the variables into two parts, we generalize Zhou's result. |
| title | A generalization of Kadell's orthogonality ex-conjecture |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2603.08041 |