Tag Archives: Polymath11

A Nice Example Related to the Frankl Conjecture

Posted on November 30, 2022 by Gil Kalai

Updates: 1. Peter Frankl brought to my attention that the very same example appeared in a paper by Dynkin and Frankl “Extremal sets of subsets satisfying conditions induced by a graph“. 2. Sam Hopkins gave a lovely reference to Ravi … Continue reading →

Posted in Combinatorics, Open discussion, Open problems | Tagged , , , , , , , , , , | 7 Comments

Amazing: Justin Gilmer gave a constant lower bound for the union-closed sets conjecture

Posted on November 17, 2022 by Gil Kalai

Frankl’s conjecture (aka the union closed sets conjecture) asserts that if is a family of subsets of [n] (=: ) which is closed under union then there is an element such that Justin Gilmer just proved an amazing weaker form … Continue reading →

Posted in Combinatorics, Open problems | Tagged , , | 22 Comments

Frankl’s Conjecture for Large Families: Ilan Karpas’ Proof

Posted on March 9, 2018 by Gil Kalai

Frankl’s conjecture asserts that a for every finite family of of finite sets that is closed under union, there is an element that belongs to at least half the sets in the family. We mentioned the problem in our very … Continue reading →

Posted in Combinatorics, Mathematics over the Internet, Open problems | Tagged , , , | 13 Comments