Zigzag stacks and m-regular linear stacks.

The contact map of a protein fold is a graph that represents the patterns of contacts in the fold. It is known that the contact map can be decomposed into stacks and queues. RNA secondary structures are special stacks in which the degree of each vertex is at most one and each arc has length of at least two.

Random K-noncrossing RNA structures.

In this paper, we introduce a combinatorial framework that provides an interpretation of RNA pseudoknot structures as sampling paths of a Markov process. Our results facilitate a variety of applications ranging from the energy-based sampling of pseudoknot structures as well as the ab initio folding via hidden Markov models. Our main result is an algorithm that generates RNA pseudoknot structures with uniform probability.