On derangement polynomials of type B. II
On derangement polynomials of type B. II
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DOI：
10.1016/j.jcta.2008.11.006
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发表时间：
2009-05
期刊：
影响因子：
--
通讯作者：
Chak-On Chow
中科院分区：
文献类型：
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作者：
Chak-On Chow
利用超八面体群Bn中超数的个数对错位进行q计数，定义了B型错位多项式。研究了错位多项式的性质，包括递归关系、母函数、实根性、互易性和由对称函数恒等式产生的单峰分解。所得结果推广和统一了Brenti、Stanley、Stembridge和Zhang等人的结果。
We define a type B derangement polynomial by q-counting derangements by the number of excedances in the hyperoctahedral group Bn. Properties of the derangement polynomial, including the recurrence relation, generating function, real-rootedness, reciprocity and a unimodal decomposition arising from a symmetric function identity, are studied. The results presented generalize and unify earlier ones due to Brenti, Stanley, Stembridge and Zhang.