On the Descent Numbers and Major Indices for the Hyperoctahedral Group
نویسنده
چکیده
Adin, Brenti, and Roichman [Adv. in Appl. Math. 27 (2001), 210–224], in answering a question posed by Foata, introduced two descent numbers and major indices for the hyperoctahedral group Bn, whose joint distribution generalizes an identity due to MacMahon and Carlitz. We shall show that yet another pair of statistics exists, and whose joint distribution constitutes a “natural” solution to Foata’s problem.
منابع مشابه
Descent Numbers and Major Indices for the Hyperoctahedral Group
We introduce and study three new statistics on the hyperoctahedral group Bn, and show that they give two generalizations of Carlitz's identity for the descent number and major index over Sn. This answers a question posed by Foata.
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تاریخ انتشار 2003