Pseudo-Permutations I: First Combinatorial and Lattice Properties

Daniel Krob Matthieu Latapy Jean-Christophe Novelli Ha Duong Phan Sylviane Schwer

To appear at Formal Power Series and Algebraic Combinatorics (FPSAC01), Tempe, Arizona (USA), May 20-26, 2001


In this paper, we introduce new combinatorial objects, the pseudo-permutations, which are a generalization of the permutations. Pseudo-permutations naturally appear in various fields of Computer Science and Mathematics. We provide the first combinatorial results on these objects: we study the classical statistics of enumeration, inversions, descents and we prove that the set of all the pseudo-permutations is a lattice.

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