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{\bf V{\'{\i}}t Jel\'{\i}nek, Nelson Y. Li, Toufik Mansour and Sherry H. F. Yan}
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{\bf Matchings Avoiding Partial Patterns and Lattice Paths}
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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.
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