Forbidden configurations and Steiner designs
Let F be a (0, 1) matrix. A (0, 1) matrix M is said to have F as a configuration if there is a submatrix of M which is a row and column permutation of F. We say that a matrix M is simple if it has no repeated columns. For a given v is an element of N, we shall denote by for b(v, F) the maximum number of columns in a simple (0, 1) matrix with v rows for which F does not occur as a configuration. We say that a matrix M is maximal for F if M has for b(v, F) columns. In this paper we show that for certain natural choices of F, for b(v, F) <= (vt)/t+1. In particular this gives an extremal characterization for Steiner t-designs as maximal (0, 1) matrices in terms of certain forbidden configurations.
forbidden configurations steiner designs nonuniform ray-chaudhuri-wilson theorem