Academic lectures: A finite embedding theorem for partial Steiner 3-designs Published date£º2014-07-16    Provided by£ºSchool of Science Title: A finite embedding theorem for partial Steiner 3-designs Guest Speaker£ºFeng Tao, Beijing Jiaotong University Time£º2014-6-23 14:00-15:00 Location£ºSY104 Content &Introduction£º  A Steiner system S(t,k,n) is a k-uniform set system on [n] for which every t-set is covered exactly once.  More generally, a partial Steiner system P(t,k,n) is a k-uniform set system on [n] where every t-set is covered at most once.  Let q be a prime power.  Using circle geometries and field-based block spreading, we give an explicit embedding for any partial Steiner system P(3,q+1,n) into a Steiner system S(3,q+1,q^m+1) for some m="m(q,n).