Sylvie Corteel
Published 2005-05-02Version 1
We derive the continued fraction form of the generating function of some new $q$-analogs of the Eulerian numbers $\hat{E}_{k,n}(q)$ introduced by Lauren Williams building on work of Alexander Postnikov. They are related to the number of alignments and weak exceedances of permutations. We show how these numbers are related to crossing and generalized patterns of permutations We generalize to the case of decorated permutations. Finally we show how these numbers appear naturally in the stationary distribution of the ASEP model.
Comments: 11 pages, 2 figures
Equidistribution and Sign-Balance on 321-Avoiding Permutations
Distribution of crossings, nestings and alignments of two edges in matchings and partitions
Matrix integrals and generating functions for permutations and one-face rooted hypermaps
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