Descent polynomials for permutations with bounded drop size

Fan Chung; Anders Claesson; Mark Dukes; Ronald Graham

Descent polynomials for permutations with bounded drop size

Fan Chung, Anders Claesson, Mark Dukes, Ronald Graham

Computer And Information Sciences

Research output: Chapter in Book/Report/Conference proceeding › Chapter

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
Title of host publication	DMTCS Proceedings
Subtitle of host publication	22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010)
Place of Publication	Nancy, France
Pages	247-258
Number of pages	12
Volume	AN
Publication status	Published - 2010

Keywords

Eulerian distribution
descent polynomial
drop size
permutations

Cite this

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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. ",

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TY - CHAP

T1 - Descent polynomials for permutations with bounded drop size

AU - Chung, Fan

AU - Claesson, Anders

AU - Dukes, Mark

AU - Graham, Ronald

PY - 2010

Y1 - 2010

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 - Eulerian distribution

KW - descent polynomial

KW - drop size

KW - permutations

UR - http://www.dmtcs.org/dmtcs-ojs/index.php/proceedings/article/view/dmAN0111

UR - http://www.dmtcs.org/dmtcs-ojs/index.php/dmtcs

M3 - Chapter

VL - AN

SP - 247

EP - 258

BT - DMTCS Proceedings

CY - Nancy, France

ER -

Descent polynomials for permutations with bounded drop size

Abstract

Keywords

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