Combinatorial Results Motivated by Computational Biology

Abstract: Under a suitable abstraction, complex biological problems can reveal surprising mathematical structure. We illustrate this phenomena with results arising from our work on RNA secondary structures. As will be explained, the combinatorics arose from attempts to understand the relationship among different RNA configurations. Toward this end, we introduce a new operation on plane trees which leads to a multipartite graph whose disjoint sets are enumerated by the Narayana numbers. Furthermore, the induced partial ordering gives us a lattice on the set of plane trees with n edges.