Progress on the union-closed conjecture and offsprings in winter 2022-2023
Combinatorics
2023-06-22 v1 History and Overview
Abstract
Mathematicians had little idea whether the easy-to-state union-closed conjecture was true or false even after 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.
Keywords
Cite
@article{arxiv.2306.12351,
title = {Progress on the union-closed conjecture and offsprings in winter 2022-2023},
author = {Stijn Cambie},
journal= {arXiv preprint arXiv:2306.12351},
year = {2023}
}
Comments
8 pages, 3 figures