Geodesic
Matchings avoiding partial patterns and lattice paths
The electronic journal of combinatorics, Tome 13 (2006)

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Zbl EuDML
In this paper, we consider matchings avoiding partial patterns $1123$ and $1132$. We give a bijection between $1123$-avoiding matchings with $n$ edges and nonnegative lattice paths from $(0,2)$ to $(2n,0)$. As a consequence, the refined enumeration of $1123$-avoiding matchings can be reduced to the enumeration of certain lattice paths. Another result of this paper is a bijection between $1132$-avoiding matchings with $n$ edges and lattice paths from $(0,0)$ to $(2n,0)$ starting with an up step, which may go under the $x$-axis.
DOI : 10.37236/1115
Classification : 05A05, 05A15, 05C30 
Vít Jelínek; Nelson Y. Li; Toufik Mansour; Sherry H. F. Yan. Matchings avoiding partial patterns and lattice paths. The electronic journal of combinatorics, Tome 13 (2006). doi: 10.37236/1115
@article{10_37236_1115,
     author = {V{\'\i}t Jel{\'\i}nek and Nelson Y. Li and Toufik Mansour and Sherry H. F. Yan},
     title = {Matchings avoiding partial patterns and lattice paths},
     journal = {The electronic journal of combinatorics},
     year = {2006},
     volume = {13},
     doi = {10.37236/1115},
     zbl = {1113.05003},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1115/}
}
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