Some progress on the #FranklConjecture!

Justin Gilmer used some information theoretic arguments to establish the first constant lower bound for the fraction of sets in a #UnionClosed family that contain the same element. Initially 1%, now 38% but it looks like some new ideas are required to get to the 50% of the conjecture.

Quanta article: https://www.quantamagazine.org/long-out-of-math-an-ai-programmer-cracks-a-pure-math-problem-20230103/

Gilmer’s paper: https://arxiv.org/abs/2211.09055