  RNA-RNA binding is an important phenomenon observed for many classes of
non-coding RNAs and plays a crucial role in a number of regulatory processes.
Recently several MFE folding algorithms for predicting the joint structure of
two interacting RNA molecules have been proposed. Here joint structure means
that in a diagram representation the intramolecular bonds of each partner are
pseudoknot-free, that the intermolecular binding pairs are noncrossing, and
that there is no so-called ``zig-zag'' configuration. This paper presents the
combinatorics of RNA interaction structures including their generating
function, singularity analysis as well as explicit recurrence relations. In
particular, our results imply simple asymptotic formulas for the number of
joint structures.
