Classifying descents according to equivalence mod k

Sergey Kitaev, Jeffrey Remmel

Research output: Contribution to conferenceAbstract

7 Citations (Scopus)

Abstract

In [5] the authors re¯ne the well-known permutation statistic \descent" by ¯xing parity of one of the descent's numbers. In this paper, we generalize the results of [5] by studying descents according to whether the ¯rst or the second element in a descent pair is equivalent to k mod k ¸ 2. We provide either an explicit or an inclusion-exclusion type formula for the distribution of the new statistics. Based on our results we obtain combinatorial proofs of a number of remarkable identities. We also provide bijective proofs of some of our results.
Original languageEnglish
Number of pages6
Publication statusPublished - 12 Jun 2006
EventPermutation Patterns Conference - Reykjavik University, Reykjavik, Iceland
Duration: 12 Jun 200616 Jun 2006

Conference

ConferencePermutation Patterns Conference
CountryIceland
CityReykjavik
Period12/06/0616/06/06

Keywords

  • classifying descents
  • permutation patterns
  • mod k

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