Forbidden configurations: Induction and linear algebra

Linear Algebra and Forbidden Configurations

Forbidden configurations and repeated induction

Over this summer, I had the great privilege of working with Dr. Richard Anstee and Ph.D. student Miguel Raggi in the problem area of forbidden configurations, a topic in extremal set theory. The induction arguments employed in our research were similar to those used by Steven Karp, Dr. Anstee’s 2008 USRA student [2]. It is convenient to use the language of matrix theory and sets for forbidden c...

On Methods of Induction in the study of Forbidden Configurations

Small Forbidden Configurations III

The present paper continues the work begun by Anstee, Ferguson, Griggs and Sali on small forbidden configurations. We define a matrix to be simple if it is a (0,1)-matrix with no repeated columns. Let F be a k× l (0,1)-matrix (the forbidden configuration). Assume A is an m×n simple matrix which has no submatrix which is a row and column permutation of F . We define forb(m,F ) as the largest n, ...

Forbidden families of configurations

A simple matrix is a (0, 1)-matrix with no repeated columns. For a (0, 1)matrix F , we say that a (0, 1)-matrix A has F as a configuration if there is a submatrix of A which is a row and column permutation of F (trace is the set system version of a configuration). Let ‖A‖ denote the number of columns of A. Let F be a family of matrices. We define the extremal function forb(m,F) = max{‖A‖ : A is...