Constructive Upper Bounds for Intersecting Set Systems

We introduce a new method for bounding the size of finite set systems with restricted intersections. We make (algorithmically fast) modifications on the set system, and the size of the resulting set system is estimated trivially. The bound for the size of the original set system is yielded by an upper bound to the increase of the rank of the intersection matrix of the set system through the modifications. lassic theorems in the field (e.g., the non-uniform versions of Ray-Chaudhuri-Wilson theorem) can be got by using certain interpolating polyomials for the modifications of the set system. f this research was done while visiting the DIMACS Center in Piscat-away, NJ.