author:  Mantaci and Roberto and Rakotondrajao and Fanja 
title:  A permutations representation that knows what "Eulerian" means 
keywords:  Permutations, subexceedant functions, exceedances, Eulerian numbers, derangements, parity of a permutaion 
abstract:  Eulerian numbers (and "Alternate Eulerian numbers") are often interpreted as distributions of statistics defined over the Symmetric group. The main purpose of this paper is to define a way to
represent permutations that provides some other combinatorial
interpretations of these numbers. This representation uses a onetoone
correspondence between permutations and the socalled
subexceedant functions.

reference: 
Mantaci and Roberto and Rakotondrajao and Fanja (2001),
A permutations representation that knows what "Eulerian" means,
Discrete Mathematics and Theoretical Computer Science 4, pp. 101108 
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pdfsource:  dm040203.pdf (81 K) 