Crossings and alignments of permutations
Sylvie Corteel
Abstract
We derive the continued fraction form of the generating function of some new q-analogs of the Eulerian numbers Ek,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.
Create a lesson
Related papers
Off-Diagonal Induced Ramsey Numbers
Bruno Andrades, Marcelo Campos, Rafael Filipe et al.
Largest Sperner families with bounded VC-dimension
Gennian Ge, Hanyu Wang, Zixiang Xu et al.
Proof of two conjectures on the log-concavity of partition ranks and cranks
Jianxi Mao, Wenle Shi, Bao-Xuan Zhu
The Exact Number of Pentagons in Book-Free Graphs
Wentao Hu
A family of symmetric counterexamples to the bent sum decomposition conjecture
Máté Róbert Kepes, Anita Kercsó-Molnár, Viczián András
Counting graphs admitting a strictly matched involution
Stephan Dominique Andres, Igor Režan