Problems in Discrete Maths Seminar
Christine Heitsch
University of Wisconsin, Madison
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.
