Matchings Avoiding Partial Patterns and Lattice Paths

Vít Jelínek, Nelson Y. Li, Toufik Mansour, Sherry H. F. Yan
2006 Electronic Journal of Combinatorics  
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,
more » ... ng with an up step, which may go under the $x$-axis.
doi:10.37236/1115 fatcat:moibgfnyaff2rh65jnxdev6uqe