Forbidden configurations and repeated induction

Abstract

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 configurations. Let [m] = {1, 2, . . . ,m}. We define a simple matrix as a (0,1)-matrix with no repeated columns. An m× n simple matrix A can be thought of a family A of n subsets S1, S2, . . . , Sn of [m] where i ∈ Sj if and only if the i, j entry of A is 1. For example, if m = 3 and A = { ∅, {2}, {3}, {1, 3}, {1, 2, 3} } , then A =  0 0 0 1 1 0 1 0 0 1 0 0 1 1 1  .

DOI: 10.1016/j.disc.2011.07.005

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Cite this paper

@article{Anstee2011ForbiddenCA, title={Forbidden configurations and repeated induction}, author={Richard P. Anstee and C. G. W. Meehan}, journal={Discrete Mathematics}, year={2011}, volume={311}, pages={2187-2197} }