Classical Combinatorics: An International Conference

Temple University, Philadelphia PA

Investigators

Abstract

Abstract The term `Classical Combinatorics,' coined by Dominique Foata, is roughly the combinatorial analog of `Classical Analysis'. Today it is better known as enumerative and algebraic combinatorics. One of the fastest-growing areas of modern mathematics, it touches upon many areas of mathematics and science, as well as forming one of the foundations of computer science. This conference will emphasize the more classical aspects of enumerative combinatorics, like permutation statistics, tableaux, q-series, words, combinatorial special function theory, commutation monoids, and related subjects, as well as their relation to computer science, physics, and statistics. Classical Combinatorics is applied in the theory of algorithms, where permutations and tableaux form the theoretical foundation for Sorting and Searching, in the theory of parallel programming, statistical physics, and many other places. To cite just one very recent example, the Foata-Zeilberger extension of Bass's evaluation of the Ihara Zeta function of a graph was used in knot theory, by Lin and Wang, to great advantage. The investigators and their colleagues study various aspects of Classical Combinatorics and use conferences as a key tool in the proliferation of new research in this area. One of the goals of Combinatorics is to find efficient methods of studying how discrete collections of objects can be arranged. The behavoir 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 conference will bring together leaders in the field and emerging researchers to discuss new ideas in the field of Combinatorics.