On RNA pseudoknot structures

We present the key ideas behind the derivation of the generating function of RNA pseudoknot structures. The latter, despite being D-finite is nonrecursive and requires therefore a novel idea -- the reflection principle -- in Weyl chambers. We discuss the combinatorics and analytic combinatorics of canoncial RNA structures and shapes and show that the character of the generating function changes with the number of mutually crossing arcs. Finally we present a linear time algorithm generating RNA pseudoknot structures with uniform probability.