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 | |
| 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.
Funding
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.
| Funders | Funder number |
|---|---|
| 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 |
Keywords
- Affine Weyl group of type A
- Juggling sequences
- Lattice point enumeration
- Root polytope
- Staircase triangulation
ASJC Scopus subject areas
- Applied Mathematics