Geodesic
Continued fractions for permutation statistics
Discrete mathematics & theoretical computer science, Permutation Patterns 2016, Tome 19 (2017-2018) no. 2.

Voir la notice de l'article provenant de la source Episciences

We explore a bijection between permutations and colored Motzkin paths that has been used in different forms by Foata and Zeilberger, Biane, and Corteel. By giving a visual representation of this bijection in terms of so-called cycle diagrams, we find simple translations of some statistics on permutations (and subsets of permutations) into statistics on colored Motzkin paths, which are amenable to the use of continued fractions. We obtain new enumeration formulas for subsets of permutations with respect to fixed points, excedances, double excedances, cycles, and inversions. In particular, we prove that cyclic permutations whose excedances are increasing are counted by the Bell numbers. 
@article{DMTCS_2018_19_2_a10,
     author = {Elizalde, Sergi},
     title = {Continued fractions for permutation statistics},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {19},
     number = {2},
     year = {2017-2018},
     doi = {10.23638/DMTCS-19-2-11},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.23638/DMTCS-19-2-11/}
}
TY  - JOUR
AU  - Elizalde, Sergi
TI  - Continued fractions for permutation statistics
JO  - Discrete mathematics & theoretical computer science
PY  - 2017-2018
VL  - 19
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.23638/DMTCS-19-2-11/
DO  - 10.23638/DMTCS-19-2-11
LA  - en
ID  - DMTCS_2018_19_2_a10
ER  - 
%0 Journal Article
%A Elizalde, Sergi
%T Continued fractions for permutation statistics
%J Discrete mathematics & theoretical computer science
%D 2017-2018
%V 19
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.23638/DMTCS-19-2-11/
%R 10.23638/DMTCS-19-2-11
%G en
%F DMTCS_2018_19_2_a10
Elizalde, Sergi. Continued fractions for permutation statistics. Discrete mathematics & theoretical computer science, Permutation Patterns 2016, Tome 19 (2017-2018) no. 2. doi : 10.23638/DMTCS-19-2-11. http://geodesic.mathdoc.fr/articles/10.23638/DMTCS-19-2-11/

Cité par Sources :