Descent polynomials for permutations with bounded drop size

Fan Chung, Anders Claesson, Mark Dukes, Ronald Graham

Research output: Chapter in Book/Report/Conference proceedingChapter


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
Title of host publicationDMTCS Proceedings
Subtitle of host publication22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010)
Place of PublicationNancy, France
Number of pages12
Publication statusPublished - 2010


  • Eulerian distribution
  • descent polynomial
  • drop size
  • permutations

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