Descent polynomials for permutations with bounded drop size

Details Descent polynomials for permutations with bounded drop size Descent polynomials for permutations with bounded drop size

2009-08-17

arxiv.org/abs/0908.2456v2

Mathematics

Combinatorics

15 pages

Scientific paper

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.

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