Classifying descents according to parity

Sergey Kitaev, Jeffrey Remmel

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)


In this paper we refine the well-known permutation statistic “descent” by fixing parity of (exactly) one of the descent’s numbers. We provide explicit formulas for the distribution of these (four) new statistics. We use certain differential operators to obtain the formulas. Moreover, we discuss connection of our new statistics to the Genocchi numbers. We also provide bijective proofs of some of our results.
Original languageEnglish
Pages (from-to)173-193
Number of pages21
JournalAnnals of Combinatorics
Issue number2
Publication statusPublished - 1 Aug 2007


  • permutation statistics
  • descents
  • parity
  • bijection
  • combinatorics


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