The Excedance Set of a Permutation

The excedance set of a permutation ?=?1?2···?n is the set of indices i for which ?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 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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