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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 \emphsubexceedant functions.
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Roberto Mantaci, Fanja Rakotondrajao. A permutations representation that knows what "Eulerian" means. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2001, 4 (2), pp.101-108. ⟨hal-00958950⟩

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