  A matching of the set $[2n]=\{ 1,2,\ldots ,2n\}$ is a partition of $[2n]$
into blocks with two elements, i.e. a graph on $[2n]$ such that every vertex
has degree one. Given two matchings $\sigma$ and $\tau$ , we say that $\sigma$
is a pattern of $\tau$ when $\sigma$ can be obtained from $\tau$ by deleting
some of its edges and consistently relabelling the remaining vertices. This is
a partial order relation turning the set of all matchings into a poset, which
will be called the matching pattern poset. In this paper, we continue the study
of classes of pattern avoiding matchings, initiated by Chen, Deng, Du, Stanley
and Yan (2007), Jelinek and Mansour (2010), Bloom and Elizalde (2012). In
particular, we work out explicit formulas to enumerate the class of matchings
avoiding two new patterns, obtained by juxtaposition of smaller patterns, and
we describe a recursive formula for the generating function of the class of
matchings avoiding the lifting of a pattern and two additional patterns.
Finally, we introduce the notion of unlabeled pattern, as a combinatorial way
to collect patterns, and we provide enumerative formulas for two classes of
matchings avoiding an unlabeled pattern of order three. In one case, the
enumeration follows from an interesting bijection between the matchings of the
class and ternary trees.
