Better bounds for the union-closed sets conjecture using the entropy approach

Abstract

We improve the best known constant $\frac{3-\sqrt{5}}{2}$ for which the union-closed conjecture is known to be true, by using dependent samples as suggested by Sawin and the entropy approach on this problem initiated by Gilmer. Meanwhile, we focus on the intuition behind this entropy approach and its boundaries.

arXiv comment12 pages There is now a verification with 2 parameters (2D) in subsection 3.4