A proof of the union-closed sets conjecture

2023/02/06 by Scandone, Raffaele
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2302.03484

Abstract

We provide a proof of the union-closed sets conjecture, by means of a suitable refinement of the breakthrough entropy-approach introduced by Gilmer. The novelty here is to consider a convex combination of A and A∪ B, where A,B are independent samples from the uniform distribution over a union-closed family.

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