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The Excedance Set of a Permutation

✍ Scribed by Richard Ehrenborg; Einar Steingrı́msson

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
124 KB
Volume
24
Category
Article
ISSN
0196-8858

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✦ Synopsis

The excedance set of a permutation π = π 1 π 2 • • • π n is the set of indices i for which π 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 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.

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