A probabilistic approach to the descent statistic

Authors:
Richard Ehrenborg;Michael Levin;Margaret A. Readdy
Affiliations:
Department of Mathematics, University of Kentucky, Lexington, Kentucky;Department of Mathematics, Harvard University, Cambridge, Massachussets;Department of Mathematics, University of Kentucky, Lexington, Kentucky
Venue:
Journal of Combinatorial Theory Series A
Year:
2002

Citing 9
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Abstract

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.