Poincaré Polynomials of Odd Diagram Classes
Authors: 
Neil Fan, Peter GuoAuthors Info & Claims
Neil Fan, Peter GuoAuthors Info & ClaimsPages 2225 - 2237
Abstract
An odd diagram class is a set of permutations with the same odd diagram. Brenti, Carnevale, and Tenner [Comb. Theory, 2 (2022), 13] 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 Poincaré 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 [Comb. Theory, 2 (2022), 13].
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Index Terms
- Poincaré Polynomials of Odd Diagram Classes
Index terms have been assigned to the content through auto-classification.
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© 2022, Society for Industrial and Applied Mathematics.
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Published: 01 January 2022
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