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

Sergey Kitaev, Toufik Mansour, Jeff Remmel

Research output: Contribution to journalArticlepeer-review


Recently, Kitaev and Remmel refined the well-known permutation statistic "descent" by fixing parity of one of the descent's numbers which was extended and generalized in several ways in the literature. In this paper, we shall fix a set partition of the natural numbers ℕ, (ℕ1,... , ℕs), and we study the distribution of descents, levels, and rises according to whether the first letter of the descent, rise, or level lies in ℕi over the set of words over the alphabet [k] = {1,...,k}. In particular, we refine and generalize some of the results by Burstein and Mansour.

Original languageEnglish
Pages (from-to)1-22
Number of pages22
JournalDiscrete Mathematics and Theoretical Computer Science
Issue number3
StatePublished - 2008


  • Composition
  • Descent
  • Level
  • Multivariate generating function
  • Rise
  • Set partition
  • Word

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science (all)
  • Discrete Mathematics and Combinatorics


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