Tag Archives: David Ellis

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

Preview: The solution by Keller and Lifshitz to several open problems in extremal combinatorics

Posted on December 10, 2017 by Gil Kalai

Peter Frankl (right) and Zoltan Furedi The news A new paper by Nathan Keller and Noam Lifshitz settles several open problems in extremal combinatorics for wide range of parameters. Those include the three problems we mention next. Three central open … Continue reading →

Posted in Combinatorics, Open problems, Updates | Tagged , , , , , , , | 1 Comment

The Simonovits-Sos Conjecture was Proved by Ellis, Filmus and Friedgut

Posted on October 25, 2010 by Gil Kalai

Simonovits and Sos asked: Let be a family of graphs with N={1,2,…,n} as the set of vertices. Suppose that every two graphs in the family have a triangle in common. How large can be? (We talked about it in this post.) … Continue reading →

Posted in Combinatorics, Open problems | Tagged , , , | 10 Comments

Extremal Combinatorics on Permutations

Posted on March 13, 2009 by Gil Kalai

We talked about extremal problems for set systems: collections of subsets of an element sets, – Sperner’s theorem, the Erdos-Ko-Rado theorem, and quite a few more. (See here, here and here.) What happens when we consider collections of permutations rather than … Continue reading →

Posted in Combinatorics | Tagged , , , , , | 9 Comments