Combinatorics Seminar: Size of the largest sum-free subset of [n]^3


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September 6, 2023 4:15 pm - 6:00 pm
MIT, Room 2-139

Saba Lepsveride & Yihang "Kimi" Sun - MIT

We prove a conjecture by Cameron and Aydinian in three dimensions, showing that the density of the largest sum-free subset of [n]^3 approaches (10 + √15)/20 as n approaches infinity. The resolution of the two-dimensional problem was accomplished by Elsholtz and Rackham in 2017. In this work, we introduce a different approach that involves considering a relaxed linear program on the projection [n]^2 and then constructing a suitable dual solution. We also explore potential approaches for addressing the higher-dimensional version of this problem.

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