Evidence for a forbidden configuration conjecture: One more case solved

A simple matrix is a (0,1)-matrix with no repeated columns. For a (0,1)matrix F , we define that a (0,1)-matrix A has no F as a configuration if there is no submatrix of A which is a row and column permutation of F . Let |A| denote the number of columns of A. We define forb(m,F ) = max{|A| : A is an m-rowed simple matrix and with no configuration F}. For two matrices H,K we define [H |K] as the concatenation of H and K. We let t ·H denote the concatenation of t copies of H. Given t ≥ 1, we define F8(t) =  1 0 1 0 0 1 0 1 1 1 0 0 1 1 0 0 t ·  1 0 0 1 1 1 0 0   . We are able to show that forb(m,F8(t)) is Θ(m2) while for any column α not contained in F8(1), we show that forb(m, [F8(t) |α]) is Ω(m3). A conjecture of Anstee and Sali predicts three 4-rowed cases to consider with quadratic bounds ∗Research supported in part by NSERC †Research supported in part by NSERC of first author ‡Some research was done while visiting UBC supported by NSERC of first author