Excedances of affine permutations

被引：4

作者：

Clark, Eric ^{[1
]}

Ehrenborg, Richard ^{[1
]}

机构：

[1] Univ Kentucky, Dept Math, Lexington, KY 40506 USA

来源：

ADVANCES IN APPLIED MATHEMATICS | 2011年 / 46卷 / 1-4期

基金：

美国国家科学基金会;

关键词：

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

D O I：

10.1016/j.aam.2009.12.006

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We introduce an excedance statistic for the group of affine permutations (G) over tilde (n) 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 (G) over tilde (n)/e(n) correspond to increasing juggling sequences and determine their Poincare series. (C) 2010 Elsevier Inc. All rights reserved.

引用

页码：175 / 191

页数：17

共 50 条

[31] EQUIDISTRIBUTIONS AROUND SPECIAL KINDS OF DESCENTS AND EXCEDANCES
Han, Bin
Mao, Jianxi
Zeng, Jiang
SIAM JOURNAL ON DISCRETE MATHEMATICS, 2021, 35 (04) : 2858 - 2879
[32] Multiple pattern avoidance with respect to fixed points and excedances
Elizalde, S
ELECTRONIC JOURNAL OF COMBINATORICS, 2004, 11 (01):
[33] An involution on derangements preserving excedances and right-to-left minima
Alexandersson, Per
Kebede, Frether Getachew
AUSTRALASIAN JOURNAL OF COMBINATORICS, 2023, 86 : 387 - 413
[34] Tableaux on k+1-cores, reduced words for affine permutations, and k-Schur expansions
Lapointe, L
Morse, J
JOURNAL OF COMBINATORIAL THEORY SERIES A, 2005, 112 (01) : 44 - 81
[35] Bijective Enumeration and Sign-Imbalance for Permutation Depth and Excedances
Eu, Sen-Peng
Fu, Tung-Shan
Lo, Yuan-Hsun
ELECTRONIC PROCEEDINGS IN THEORETICAL COMPUTER SCIENCE, 2024, (403):
[36] Counting derangements with signed right-to-left minima and excedances
Pei, Yanni
Zeng, Jiang
ADVANCES IN APPLIED MATHEMATICS, 2024, 152
[37] The Construction of Orthomorphic Permutations on Linearorthomorphic Permutations
Liao, Dajian
PROCEEDINGS OF ANNUAL CONFERENCE OF CHINA INSTITUTE OF COMMUNICATIONS, 2010, : 264 - 267
[38] Simple permutations and pattern restricted permutations
Albert, MH
Atkinson, MD
DISCRETE MATHEMATICS, 2005, 300 (1-3) : 1 - 15
[39] Ballot permutations and odd order permutations
Spiro, Sam
DISCRETE MATHEMATICS, 2020, 343 (06)
[40] Permutations, lattice permutations, and the hypergeometric series
MacMahon, PA
PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 1921, 19 : 216 - 227

← 1 2 3 4 5 →