Discrete Mathematics & Theoretical Computer Science, Vol 4, No 2 (2001)

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A permutations representation that knows what "Eulerian" means

Roberto Mantaci, Fanja Rakotondrajao

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.

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