A probabilistic approach to the descent statistic

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13 Scopus citations


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.

Original languageEnglish
Article number93233
Pages (from-to)150-162
Number of pages13
JournalJournal of Combinatorial Theory. Series A
Issue number1
StatePublished - 2002

Bibliographical note

Funding Information:
This work was supported by NSF Grants DMS 96-19681 and DMS 99-83660. The first author was also partially supported by NSF Grant DMS 98-00910. Levin’s research was directed by Ehrenborg and Readdy, and supported by the National Science Foundation through the Research Experiences for Undergraduates (REU) program at Cornell University in summer 2000.

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics


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