One of the fundamental problems in Extremal Combinatorics concerns maximal set systems with forbidden subconfigurations. One such open problem concerns the conjecture due to Anstee and Sali on the order of maximal configurations with certain forbidden subconfigurations. I shall talk about some well known results, talk about the Anstee-Sali conjecture, and finally talk about some of my recent work concerning Steiner designs occuring as maximal forbidden configurations for certain natural choices of subconfigrations. This generalizes a result of Anstee and Barekat.

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Last updated: 14 Jul 2024