Zeilberger-Bressoud $q$-Dyson定理的对称函数推广

arXiv: Combinatorics Pub Date : 2020-09-10 DOI:10.1090/proc/15399

Yue Zhou

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引用次数: 0

摘要

2000年，Kadell给出了Zeilberger- Bressoud $q$-Dyson定理或$q$-Dyson常数项恒等式的对称函数推广的正交性猜想。Karolyi, Lascoux和Warnaar在2015年证明了这一猜想。本文通过稍微改变Kadell猜想的变量，得到了q -Dyson常数项恒等式的另一种对称函数推广。这个新的广义常数项可以用简单的乘积形式表示。

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A symmetric function generalization of the Zeilberger–Bressoud $q$-Dyson theorem

In 2000, Kadell gave an orthogonality conjecture for a symmetric function generalization of the Zeilberger--Bressoud $q$-Dyson theorem or the $q$-Dyson constant term identity. This conjecture was proved by Karolyi, Lascoux and Warnaar in 2015. In this paper, by slightly changing the variables of Kadell's conjecture, we obtain another symmetric function generalization of the $q$-Dyson constant term identity. This new generalized constant term admits a simple product-form expression.

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arXiv: Combinatorics

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