Large Forbidden Configurations and Design Theory
نویسندگان
چکیده
Let forb(m,F ) denote the maximum number of columns possible in a (0,1)matrix A that has no repeated columns and has no submatrix which is a row and column permutation of F . We consider cases where the configuration F has a number of columns that grows with m. For a k× ` matrix G, define s ·G to be the concatenation of s copies of G. In a number of cases we determine forb(m,mα ·G) is Θ(mk+α). Results of Keevash on the existence of designs provide constructions that provide asymptotic lower bounds. An induction idea of Anstee and Lu is useful in obtaining upper bounds.
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