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.