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

Producción científica: Article › revisión exhaustiva

7 Citas (Scopus)

Resumen

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.

Idioma original	English
Páginas (desde-hasta)	175-191
Número de páginas	17
Publicación	Advances in Applied Mathematics
Volumen	46
N.º	1-4
DOI	https://doi.org/10.1016/j.aam.2009.12.006
Estado	Published - ene 2011

Nota bibliográfica

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.

Financiación

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.

Financiadores	Número del financiador
U.S. Department of Energy Chinese Academy of Sciences Guangzhou Municipal Science and Technology Project Oak Ridge National Laboratory Extreme Science and Engineering Discovery Environment National Science Foundation National Energy Research Scientific Computing Center National Natural Science Foundation of China	DMS 0902063

ASJC Scopus subject areas

Applied Mathematics

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10.1016/j.aam.2009.12.006

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

author = "Eric Clark and Richard Ehrenborg",

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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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JO - Advances in Applied Mathematics

JF - Advances in Applied Mathematics

IS - 1-4

ER -

Excedances of affine permutations

Resumen

Nota bibliográfica

Financiación

ASJC Scopus subject areas

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