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Tag Archives: Peter Frankl
Greetings from Oberwolfach. This week, there is a great meeting here on combinatorics. In this post I want to state the Brown-Erdős-Sós conjecture and one of its variants. The trigger was a beautiful talk I heard from Lior Gishboliner on … Continue reading
With Tolya (Anatoly) Vershik, Saint Petersburg, 2003 Peter Frankl and Voita (Vojtěch) Rödl, NYC, summer 1986 (or 1987). This post mentions the Frankl-Rödl theorem. Jeroen Zuiddam at IAS, a few days ago. (See this post) We just moved to a … Continue reading
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
Hardness of Approximating Vertex Cover, Polytope-Integrality-Gap, the Alswede-Kachatrian theorem, and More.
Lior Silberman asked about applications of the 2-to-2 game theorem to hardness of approximation, and James Lee answered mentioning applications to vertex cover. Let me elaborate a little on vertex cover, and other matters. (Here is the pervious post on … Continue reading
Frankl’s conjecture Frankl’s conjecture is the following: Let be a finite family of finite subsets of which is closed under union, namely, if then also . Then there exists an element which belongs to at least half the sets in . … Continue reading
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
Update (Jan 21) j) Polymath11 (?) Tim Gowers’s proposed a polymath project on Frankl’s conjecture. If it will get off the ground we will have (with polymath10) two projects running in parallel which is very nice. (In the comments Jon Awbrey gave … Continue reading
Noga with Uri Feige among various other heroes A few weeks ago I devoted a post to the 240-summit conference for Péter Frankl, Zoltán Füredi, Ervin Győri and János Pach, and today I will bring you the slides of Noga … Continue reading
Rick Wilson The Frankl-Wilson theorem is a remarkable theorem with many amazing applications. It has several proofs, all based on linear algebra methods (also referred to as dimension arguments). The original proof is based on a careful study of incidence … Continue reading
1. About: My name is Gil Kalai and I am a mathematician working mainly in the field of Combinatorics. Within combinatorics, I work mainly on geometric combinatorics and the study of convex polytopes and related objects, and on the analysis of Boolean functions … Continue reading