Mathematical Foundations of Computer Science & Discrete Mathematics

In the area of geometric configurations we have investigated weakly flag-transitive configurations and found a one-to-one correspondence with bipartite 1-arc transitive graphs with girth 6 or more. Such graphs are line graphs of 1-regular cubic cyclic Haar graphs. Our results have applications in mathematical chemistry where they imply that hexagonal molecular graphs on the torus which have this type of symmetry are intrinsically chiral. We have obtained interesting results on Euler embeddings of 2-connected 4-valent graphs into orientable surfaces, and determined automorphism groups of Walecki tournaments which have no aperiodic binary subsequences. We have developed and implemented a Gosper-type algorithm for closed-form summation of multibasic and mixed hypergeometric terms. We have also designed high-performance memory modules which solve the membership problem in constant time and near-optimal space.