Crossing and alignments of permutations

Details Crossing and alignments of permutations Crossing and alignments of permutations

2006-01-19

arxiv.org/abs/math/0601469v1

Mathematics

Combinatorics

Scientific paper

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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