MIT-Harvard-MSR Combinatorics Seminar: Threshold for Steiner triple systems


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April 20, 2022 4:15 pm - 5:15 pm
MIT, Room 2-139

Mehtaab Sawhney - MIT

We prove that with high probability $G^{(3)}(n,n^{-1+o(1)})$ contains a  spanning Steiner triple system. We also prove the analogous result for  spanning Latin squares. This threshold is sharp up to a subpolynomial  factor. Our result follows from a novel bootstrapping scheme that utilizes  iterative absorption as well as recent connections which have been  established between thresholds and spread measures. Joint work with Ashwin  Sah and Michael Simkin.