A permutations representation that knows what "Eulerian" means - Roberto Mantaci; Fanja Rakotondrajao (Discrete Mathematics & Theoretical Computer Science, 2001)
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 \emphsubexceedant functions.