Descent polynomials for permutations with bounded drop size

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. (C) 2010 Elsevier Ltd. All rights reserved.