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  1. Home > Articles & Issues >
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  3. Descent polynomials ...
Conference paper

Descent polynomials for permutations with bounded drop size

Fan Chung (1), Anders Claesson (2), Mark Dukes ORCID (3) (4), Ronald Graham (1)
(1) University of California [San Diego]
(2) The Mathematics Institute, Reyjavik University
(3) Science Institute, University of Iceland
(4) University of Iceland [Reykjavik]
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Imported on
January 31, 2017
Published on
December 31, 2009
Last modified on
March 31, 2025
Volume
DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010)
Proceedings
DOI
10.46298/dmtcs.2856
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https://about.hal.science/hal-authorisation-v1
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Descent polynomials for permutations with bounded drop size

Fan Chung (1), Anders Claesson (2), Mark Dukes ORCID (3) (4), Ronald Graham (1)
(1) University of California [San Diego]
(2) The Mathematics Institute, Reyjavik University
(3) Science Institute, University of Iceland
(4) University of Iceland [Reykjavik]
Abstract
English
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.
French
Motivés par les "suites de jonglerie'' et le tri à bulles, nous étudions les permutations de l'ensemble ${1, 2, \ldots, n}$ ayant $d$ descentes et une taille de déficience maximale $k$. Nous donnons des formules explicites pour l'énumération de telles permutations pour des entiers k et d fixés, ainsi que les fonctions génératrices connexes. Nous montrons aussi que les coefficients possèdent des propriétés d'unimodalité et de symétrie.
Keywords
  • [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO]
  • [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]
  • Permutations
  • descent polynomial
  • drop size
  • Eulerian distribution.
Cited by

Source: OpenCitations

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