The Excedance Set of a Permutation

Authors: Ehrenborg R.¹; Steingrímsson E.²

Source: Advances in Applied Mathematics, Volume 24, Number 3, April 2000 , pp. 284-299(16)

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Abstract:

The excedance set of a permutation = ₁₂ sdot sdot sdot _n is the set of indices i for which _i > i. 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 Sscr _n is {1,2 ,…, lfloor n/2 rfloor }. We also relate certain excedance set numbers to Stirling numbers of the second kind, and others to the Genocchi numbers. Copyright 2000 Academic Press.

Language: English

Document Type: Research article

Affiliations: 1: School of Mathematics, Institute for Advanced Study, Olden Lane, Princeton, New Jersey, 08540 2: Department of Mathematics, Chalmers University of Technology, Göteborg, S-412 96, Sweden

Publication date: 2000-04-01