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arXiv · 2306.12351

Progress on the union-closed conjecture and offsprings in winter 2022-2023

Stijn Cambie
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Abstract

Mathematicians had little idea whether the easy-to-state union-closed conjecture was true or false even after $40$ years. However, last winter saw a surge of interest in the conjecture and its variants, initiated by the contribution of a researcher at Google. Justin Gilmer [arXiv:2211.09055] made a significant breakthrough by discovering a first constant lower bound for the proportion of the most common element in a union-closed family.

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Stijn Cambie. 2023-06-21. Progress on the union-closed conjecture and offsprings in winter 2022-2023. https://arxiv.org/abs/2306.12351

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