Descent polynomials for permutations with bounded drop size

Fan Chung; Anders Claesson; Mark Dukes; Ronald Graham

doi:10.1016/j.ejc.2010.01.011

Descent polynomials for permutations with bounded drop size

Fan Chung
, Anders Claesson
, Mark Dukes
, Ronald Graham

Faculty of Physical Sciences

University of Iceland

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	1853-1867
Number of pages	15
Journal	European Journal of Combinatorics
Volume	31
Issue number	7
DOIs	https://doi.org/10.1016/j.ejc.2010.01.011
Publication status	Published - Oct 2010

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@article{f4eb8f65568845099c63956375081331,

title = "Descent polynomials for permutations with bounded drop size",

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.",

author = "Fan Chung and Anders Claesson and Mark Dukes and Ronald Graham",

note = "Funding Information: AC and MD were supported by grant no. 090038011 from the Icelandic Research Fund.",

year = "2010",

month = oct,

doi = "10.1016/j.ejc.2010.01.011",

language = "English",

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T1 - Descent polynomials for permutations with bounded drop size

AU - Chung, Fan

AU - Claesson, Anders

AU - Dukes, Mark

AU - Graham, Ronald

N1 - Funding Information: AC and MD were supported by grant no. 090038011 from the Icelandic Research Fund.

PY - 2010/10

Y1 - 2010/10

N2 - 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.

AB - 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.

UR - https://www.scopus.com/pages/publications/77955315365

U2 - 10.1016/j.ejc.2010.01.011

DO - 10.1016/j.ejc.2010.01.011

M3 - Article

SN - 0195-6698

VL - 31

SP - 1853

EP - 1867

JO - European Journal of Combinatorics

JF - European Journal of Combinatorics

IS - 7

ER -

Descent polynomials for permutations with bounded drop size

Abstract

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