Symbolic Computation and Combinatorics

Temple University, Philadelphia PA

Investigators

Abstract

Doron Zeilberger proposes to continue to develop methodologies for harnessing the great potential of Symbolic Computation to do research in Combinatorics and related areas. In particular he hopes to introduce new computational and conceptual frameworks that would extend the so-called Wilf-Zeilberger proof theory to much wider classes of identities and theorems. He also proposes to continue his efforts in `Artificial Combinatorics', and develop algorithms for the discovery and {\it rigorous} proof of theorems in combinatorics whose complexity make them unfeasible for human proofs. This research should be symbiotic, as it is expected that both the concrete results and the underlying methodologies, would help computer algebra developers to improve and enhance their systems. This research is in the general area of Combinatorics. One of the goals of Combinatorics is to find efficient methods of studying how discrete collections of objects can be arranged. The behavior of discrete systems is extremely important to modern communications. For example, the design of large networks, such as those occurring in telephone systems, and the design of algorithms in computer science deal with discrete sets of objects, and this makes use of combinatorial research. This research is also in the general area of Symbolic Computation, that attempts to teach computers to perform research that previously required extensive human resources. Progress in this area promises to have important ramifications to science and technology.