  Recently, Chen et al. derived the generating function for partitions avoiding
right nestings and posed the problem of finding the generating function for
partitions avoiding right crossings. In this paper, we derive the generating
function for partitions avoiding right crossings via an intermediate structure
of partial matchings avoiding 2-right crossings and right nestings. We show
that there is a bijection between partial matchings avoiding 2-right crossing
and right nestings and partitions avoiding right crossings.
