Descent polynomials for permutations with bounded drop size

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.

• Type: Journal
• Year: 2010
• Where: EJC
• Authors: Fan R. K. Chung, Anders Claesson, Mark Dukes, Ronald L. Graham
• Keywords: Bubble Sort, EJC 2007, EJC 2010, Maximum Drop Size, Permutations