✦ LIBER ✦

A Probabilistic Approach to the Descent Statistic

✍ Scribed by Richard Ehrenborg; Michael Levin; Margaret A. Readdy

Publisher: Elsevier Science
Year: 2002
Tongue: English
Weight: 117 KB
Volume: 98
Category: Article
ISSN: 0097-3165
DOI: 10.1006/jcta.2001.3233

No coin nor oath required. For personal study only.

✦ Synopsis

We present a probabilistic approach to studying the descent statistic based upon a two-variable probability density. This density is log concave and, in fact, satisfies a higher order concavity condition. From these properties we derive quadratic inequalities for the descent statistic. Using Fourier series, we give exact expressions for the Euler numbers and the alternating r-signed permutations. We also obtain a probabilistic interpretation of the sin function.

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