The excedance set of a permutation

Richard Ehrenborg; Einar Steingrímsson

doi:10.1006/aama.1999.0671

The excedance set of a permutation

Richard Ehrenborg, Einar Steingrímsson

Mathematics

Research output: Contribution to journal › Article › peer-review

26 Scopus citations

Abstract

The excedance set of a permutation π=π₁π₂···π_n is the set of indices i for which π_ii. 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 S_n 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	https://doi.org/10.1006/aama.1999.0671
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.

ASJC Scopus subject areas

Applied Mathematics

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10.1006/aama.1999.0671

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N2 - 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.

AB - 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.

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The excedance set of a permutation

Abstract

Bibliographical note

ASJC Scopus subject areas

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