Fan Chung ; Anders Claesson ; Mark Dukes ; Ronald Graham
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Descent polynomials for permutations with bounded drop size
dmtcs:2856 -
Discrete Mathematics & Theoretical Computer Science,
January 1, 2010,
DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010)
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https://doi.org/10.46298/dmtcs.2856
Descent polynomials for permutations with bounded drop size
Authors: Fan Chung 1; Anders Claesson 2; Mark Dukes 3,4; Ronald Graham 1
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Fan Chung;Anders Claesson;Mark Dukes;Ronald Graham
1 University of California [San Diego]
2 The Mathematics Institute, Reyjavik University
3 Science Institute, University of Iceland
4 University of Iceland [Reykjavik]
Motivated by juggling sequences and bubble sort, we examine permutations on the set${1, 2, \ldots, n}$ 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.