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Descent polynomials for permutations with bounded drop size

Chung, Fan and Claesson, Anders and Dukes, Mark and Graham, Ronald (2010) Descent polynomials for permutations with bounded drop size. In: DMTCS Proceedings. Discrete Mathematics & Theoretical Computer Science, Nancy, France, pp. 247-258.

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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.