Poincaré Polynomials of Odd Diagram Classes
Poincaré Polynomials of Odd Diagram Classes
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DOI：
10.1137/22m1470517
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发表时间：
2021
期刊：
影响因子：
--
通讯作者：
Peter L. Guo
中科院分区：
文献类型：
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作者：
Neil J.Y. Fan;Peter L. Guo
An odd diagram class is a set of permutations with the same odd diagram. Brenti, Carnevale and Tenner showed that each odd diagram class is an interval in the Bruhat order. They conjectured that such intervals are rank-symmetric. In this paper, we present an algorithm to partition an odd diagram class in a uniform manner. As an application, we obtain that the Poincar'e polynomial of an odd diagram class factors into polynomials of the form $1+t+cdots+t^m$. This in particular resolves the conjecture of Brenti, Carnevale and Tenner.
