Excedances of affine permutations

Eric Clark, Richard Ehrenborg

Research output: Contribution to journalArticlepeer-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 languageEnglish
Pages (from-to)175-191
Number of pages17
JournalAdvances in Applied Mathematics
Volume46
Issue number1-4
DOIs
StatePublished - 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

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