English

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 4040 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