English

Descent polynomials for permutations with bounded drop size

Combinatorics 2010-01-18 v2

Abstract

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.

Keywords

Cite

@article{arxiv.0908.2456,
  title  = {Descent polynomials for permutations with bounded drop size},
  author = {Fan Chung and Anders Claesson and Mark Dukes and Ron Graham},
  journal= {arXiv preprint arXiv:0908.2456},
  year   = {2010}
}

Comments

15 pages

R2 v1 2026-06-21T13:36:16.525Z