Descent polynomials for permutations with bounded drop size

Fan Chung, Anders Claesson, Mark Dukes, Ronald Graham

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)


Motivated by juggling sequences and bubble sort, we examine permutations on the set {1,2,…,n} with d descents and maximum drop size k. We give explicit formulas for enumerating such permutations for given integers k and d. We also derive the related generating functions and prove unimodality and symmetry of the coefficients.
Original languageEnglish
Pages (from-to)1853-1867
Number of pages15
JournalEuropean Journal of Combinatorics
Issue number7
Publication statusPublished - Oct 2010


  • juggling sequences
  • coefficients
  • statistics
  • permutations


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