Crossing and alignments of permutations

2006/01/19 by Sylvie Corteel, Corteel, Sylvie · 1 citation
Computer Science · Mathematics · #05A17 #Bayesian Methods and Mixture Models #Combinatorics (math.CO) #FOS: Mathematics #Random Matrices and Applications #Stochastic processes and statistical mechanics

paper · doi:10.48550/arxiv.math/0601469

openalex publication_date 2006/01/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Cited by

• An involution for trivariate symmetries of vincular patterns

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