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Pré-Publication, Document De Travail Année : 2006

Crossing and alignments of permutations

Sylvie Corteel
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Résumé

We introduce the notion of crossings and nestings of a permutation. We compute the generating function of permutations with a fixed number of weak exceedances, crossings and nestings. We link alignments and permutation patterns to these statistics. We generalize to the case of decorated permutations. Finally we show how this is related to the stationary distribution of the Partially ASymmetric Exclusion Process (PASEP) model.
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Dates et versions

hal-00004825 , version 1 (03-05-2005)
hal-00004825 , version 2 (19-01-2006)

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Sylvie Corteel. Crossing and alignments of permutations. 2006. ⟨hal-00004825v2⟩
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