Abstract
The excedance set of a permutation π=π1π2···πn is the set of indices i for which πii. We give a formula for the number of permutations with a given excedance set and recursive formulas satisfied by these numbers. We prove log-concavity of certain sequences of these numbers and we show that the most common excedance set among permutations in the symmetric group Sn is 1,2,...,⌊n/2⌋. We also relate certain excedance set numbers to Stirling numbers of the second kind, and others to the Genocchi numbers.
| Original language | English |
|---|---|
| Pages (from-to) | 284-299 |
| Number of pages | 16 |
| Journal | Advances in Applied Mathematics |
| Volume | 24 |
| Issue number | 3 |
| DOIs | |
| State | Published - Apr 2000 |
Bibliographical note
Funding Information:The authors thank Margaret Readdy who read an earlier version of this paper. The rst author was in part supported by National Science Foundation, DMS 97-29992, and NEC Research Institute, Inc.
Funding
The authors thank Margaret Readdy who read an earlier version of this paper. The rst author was in part supported by National Science Foundation, DMS 97-29992, and NEC Research Institute, Inc.
| Funders | Funder number |
|---|---|
| National Science Foundation (NSF) | DMS 97-29992 |
ASJC Scopus subject areas
- Applied Mathematics