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

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

15 Citations (Scopus)

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

Keywords

juggling sequences
coefficients
statistics
permutations

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10.1016/j.ejc.2010.01.011

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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.",

keywords = "juggling sequences, coefficients, statistics, permutations",

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

year = "2010",

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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

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.

KW - juggling sequences

KW - coefficients

KW - statistics

KW - permutations

U2 - 10.1016/j.ejc.2010.01.011

DO - 10.1016/j.ejc.2010.01.011

M3 - Article

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

Keywords

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