Geodesic
Matchings avoiding partial patterns
The electronic journal of combinatorics, Tome 13 (2006)
Cet article a éte moissonné depuis la source The Electronic Journal of Combinatorics website

Voir la notice de l'article

We show that matchings avoiding a certain partial pattern are counted by the $3$-Catalan numbers. We give a characterization of $12312$-avoiding matchings in terms of restrictions on the corresponding oscillating tableaux. We also find a bijection between matchings avoiding both patterns $12312$ and $121323$ and Schröder paths without peaks at level one, which are counted by the super-Catalan numbers or the little Schröder numbers. A refinement of the super-Catalan numbers is derived by fixing the number of crossings in the matchings. In the sense of Wilf-equivalence, we use the method of generating trees to show that the patterns 12132, 12123, 12321, 12231, 12213 are all equivalent to the pattern $12312$.
DOI : 10.37236/1138
Classification : 05A05, 05A15, 05C30
Mots-clés : oscillating tableaux, Schröder numbers, Schröder paths, super-Catalan numbers 
@article{10_37236_1138,
     author = {William Y. C. Chen and Toufik Mansour and Sherry H. F. Yan},
     title = {Matchings avoiding partial patterns},
     journal = {The electronic journal of combinatorics},
     year = {2006},
     volume = {13},
     doi = {10.37236/1138},
     zbl = {1112.05001},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1138/}
}
TY  - JOUR
AU  - William Y. C. Chen
AU  - Toufik Mansour
AU  - Sherry H. F. Yan
TI  - Matchings avoiding partial patterns
JO  - The electronic journal of combinatorics
PY  - 2006
VL  - 13
UR  - http://geodesic.mathdoc.fr/articles/10.37236/1138/
DO  - 10.37236/1138
ID  - 10_37236_1138
ER  - 
%0 Journal Article
%A William Y. C. Chen
%A Toufik Mansour
%A Sherry H. F. Yan
%T Matchings avoiding partial patterns
%J The electronic journal of combinatorics
%D 2006
%V 13
%U http://geodesic.mathdoc.fr/articles/10.37236/1138/
%R 10.37236/1138
%F 10_37236_1138
William Y. C. Chen; Toufik Mansour; Sherry H. F. Yan. Matchings avoiding partial patterns. The electronic journal of combinatorics, Tome 13 (2006). doi: 10.37236/1138

Cité par Sources :