A Steiner system S(t, k, v) is a set X of v points, and a collection of subsets of X of size k (called blocks), such that any t points of X are in exactly one of the blocks. The special case t = 2 and k = 3 corresponds to a so-called Steiner triple system. For a projective plane, v = n^2 + n + 1, k = n + 1, t = 2, and the blocks are simply lines. The number r of blocks containing a point in a S(t, k, v) Steiner system is independent of the point.

automorphism group | configuration | Mathieu groups | simple group | Steiner quadruple system | Steiner triple system | t-design | transitive group

Jakob Steiner