Geodesic
Avoiding patterns in irreducible permutations
Discrete mathematics & theoretical computer science, Tome 17 (2015-2016) no. 3.

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

We explore the classical pattern avoidance question in the case of irreducible permutations, <i>i.e.</i>, those in which there is no index $i$ such that $\sigma (i+1) - \sigma (i)=1$. The problem is addressed completely in the case of avoiding one or two patterns of length three, and several well known sequences are encountered in the process, such as Catalan, Motzkin, Fibonacci, Tribonacci, Padovan and Binary numbers. Also, we present constructive bijections between the set of Motzkin paths of length $n-1$ and the sets of irreducible permutations of length $n$ (respectively fixed point free irreducible involutions of length $2n$) avoiding a pattern $\alpha$ for $\alpha \in \{132,213,321\}$. This induces two new bijections between the set of Dyck paths and some restricted sets of permutations. 
@article{DMTCS_2016_17_3_a14,
     author = {Baril, Jean-Luc},
     title = {Avoiding patterns in irreducible permutations},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {17},
     number = {3},
     year = {2015-2016},
     doi = {10.46298/dmtcs.2158},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2158/}
}
TY  - JOUR
AU  - Baril, Jean-Luc
TI  - Avoiding patterns in irreducible permutations
JO  - Discrete mathematics & theoretical computer science
PY  - 2015-2016
VL  - 17
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2158/
DO  - 10.46298/dmtcs.2158
LA  - en
ID  - DMTCS_2016_17_3_a14
ER  - 
%0 Journal Article
%A Baril, Jean-Luc
%T Avoiding patterns in irreducible permutations
%J Discrete mathematics & theoretical computer science
%D 2015-2016
%V 17
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2158/
%R 10.46298/dmtcs.2158
%G en
%F DMTCS_2016_17_3_a14
Baril, Jean-Luc. Avoiding patterns in irreducible permutations. Discrete mathematics & theoretical computer science, Tome 17 (2015-2016) no. 3. doi : 10.46298/dmtcs.2158. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2158/

Cité par Sources :