Some approaches to solve General (t,k) design existence problem and other related problems

Amitava Bhattacharya

Abstract

In this talk we consider some approaches that can be used to solve the generalized (t,k) design problem. Special cases of the generalized (t,k) design problem include t-designs, degree sequences of graphs and hypergraphs, partial Steiner systems etc. Some related problems like characterization of f-vectors of pure simplicial complexes are also well known but little understood. In this talk we will suggest how enumerative and polyhedral techniques may help.