Counting descents, rises, and levels, with prescribed first element, in words

Sergey Kitaev, Toufik Mansour, Jeffrey Remmel

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

Recently, Kitaev and Remmel [9] re¯ned the well-known permutation statistic \descent" by ¯xing parity of one of the descent's numbers. Results in [9] were extended and generalized in several ways in [7, 10, 11, 12]. In this paper, we shall ¯x a set partition of the natural numbers N, (N1; : : : ;Ns), and we study the distribution of descents, levels, and rises according to whether the ¯rst letter of the descent, rise, or level lies in Ni over the set of words over the alphabet [k] = f1; : : : ; kg. In particular, we re¯ne and generalize some of the results in [4].
Original languageEnglish
Number of pages22
JournalDiscrete Mathematics and Theoretical Computer Science
Volume10
Issue number3
Publication statusPublished - 2008

Keywords

  • distribution of descents
  • rises
  • levels
  • permutation statistics

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