The excedance set of a permutation

Richard Ehrenborg, Einar Steingrímsson

Research output: Contribution to journalArticlepeer-review

26 Scopus citations


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 languageEnglish
Pages (from-to)284-299
Number of pages16
JournalAdvances in Applied Mathematics
Issue number3
StatePublished - 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.

ASJC Scopus subject areas

  • Applied Mathematics


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