Excedances of affine permutations

Eric Clark; Richard Ehrenborg

doi:10.1016/j.aam.2009.12.006

Excedances of affine permutations

Eric Clark, Richard Ehrenborg

Mathematics

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

7 Citations (SciVal)

Abstract

We introduce an excedance statistic for the group of affine permutations and determine the generating function of its distribution. The proof involves working with enumerating lattice points in a skew version of the root polytope of type A. We also show that the left coset representatives of the quotient correspond to increasing juggling sequences and determine their Poincaré series.

Original language	English
Pages (from-to)	175-191
Number of pages	17
Journal	Advances in Applied Mathematics
Volume	46
Issue number	1-4
DOIs	https://doi.org/10.1016/j.aam.2009.12.006
State	Published - Jan 2011

Bibliographical note

Funding Information:
The authors thank Serkan Hosten for introducing us to the reference [1] and our referee for his comments. Special thanks to Margaret Readdy and Ruriko Yoshida who read earlier versions of this paper. The second author was supported by National Science Foundation grant DMS 0902063.

Keywords

Affine Weyl group of type A
Juggling sequences
Lattice point enumeration
Root polytope
Staircase triangulation

ASJC Scopus subject areas

Applied Mathematics

Access to Document

10.1016/j.aam.2009.12.006

Cite this

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title = "Excedances of affine permutations",

abstract = "We introduce an excedance statistic for the group of affine permutations and determine the generating function of its distribution. The proof involves working with enumerating lattice points in a skew version of the root polytope of type A. We also show that the left coset representatives of the quotient correspond to increasing juggling sequences and determine their Poincar{\'e} series.",

keywords = "Affine Weyl group of type A, Juggling sequences, Lattice point enumeration, Root polytope, Staircase triangulation",

author = "Eric Clark and Richard Ehrenborg",

note = "Funding Information: The authors thank Serkan Hosten for introducing us to the reference [1] and our referee for his comments. Special thanks to Margaret Readdy and Ruriko Yoshida who read earlier versions of this paper. The second author was supported by National Science Foundation grant DMS 0902063.",

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AU - Ehrenborg, Richard

N1 - Funding Information: The authors thank Serkan Hosten for introducing us to the reference [1] and our referee for his comments. Special thanks to Margaret Readdy and Ruriko Yoshida who read earlier versions of this paper. The second author was supported by National Science Foundation grant DMS 0902063.

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N2 - We introduce an excedance statistic for the group of affine permutations and determine the generating function of its distribution. The proof involves working with enumerating lattice points in a skew version of the root polytope of type A. We also show that the left coset representatives of the quotient correspond to increasing juggling sequences and determine their Poincaré series.

AB - We introduce an excedance statistic for the group of affine permutations and determine the generating function of its distribution. The proof involves working with enumerating lattice points in a skew version of the root polytope of type A. We also show that the left coset representatives of the quotient correspond to increasing juggling sequences and determine their Poincaré series.

KW - Affine Weyl group of type A

KW - Juggling sequences

KW - Lattice point enumeration

KW - Root polytope

KW - Staircase triangulation

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SP - 175

EP - 191

JO - Advances in Applied Mathematics

JF - Advances in Applied Mathematics

IS - 1-4

ER -

Excedances of affine permutations

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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Cite this