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q-Eulerian Polynomials Arising from Coxeter Groups

✍ Scribed by Francesco Brenti

Book ID: 102967909
Publisher: Elsevier Science
Year: 1994
Tongue: English
Weight: 640 KB
Volume: 15
Category: Article
ISSN: 0195-6698
DOI: 10.1006/eujc.1994.1046

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✦ Synopsis

We study the polynomials obtained by enumerating a finite Coxeter group by number of descents. The type (A) case gives rise to the familiar Eulerian polynomials, while the (B) and (D) cases provide two new (q)-analogues. Various recursion relations, generating functions and unimodality properties are derived, which generalize and unify earlier results of Dolgachev, Lunts, Stanley and Stembridge.

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