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.
|Number of pages||16|
|Journal||Advances in Applied Mathematics|
|State||Published - Apr 2000|
Bibliographical noteFunding 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.
ASJC Scopus subject areas
- Applied Mathematics