Descent polynomials for permutations with bounded drop size

Authors:
Fan Chung;Anders Claesson;Mark Dukes;Ronald Graham
Affiliations:
University of California at San Diego, La Jolla CA 92093, USA;The Mathematics Institute, School of Computer Science, Reykjavik University, 103 Reykjavik, Iceland;Science Institute, University of Iceland, 107 Reykjavik, Iceland;University of California at San Diego, La Jolla CA 92093, USA
Venue:
European Journal of Combinatorics
Year:
2010

Citing 1
Cited 1

Concrete Math

Concrete Math

Inversion-descent polynomials for restricted permutations

Journal of Combinatorial Theory Series A

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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.