A permutations representation that knows what " Eulerian" means

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 one-to-one correspondence between permutations and the so-called subexceedant functions.