Forbidden Configurations: An update - Richard Anstee

I'll review some results about Forbidden Configurations while introducing a conjecture. Let F be a k x l (0,1)-matrix. We define a matrix to be simple if it is a (0,1)-matrix with no repeated columns.  We say that a simple matrix A has no F-configuration if no submatrix of A is a row and column permutation of F. We are interested in the extremal function forb(m,F) which is the maximum number of columns in an m-rowed simple matrix that has no F-configuration.  A conjecture of Sali and A. predicts the asymptotic behaviour of forb(m,F) for fixed F as m tends to infinity by identifying some easy but seemingly important constructions.   With Keevash, we developed a stability result for k-uniform t-intersecting set systems that determines forb(m,F) for F being k x 2. With Fleming, Furedi and Sali, we have a linear algebra argument for all but `one' k x l F where forb(m,F) is O(mk-1)