Tag Archives: Peter Frankl

A Nice Example Related to the Frankl Conjecture

Update: 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“. The example As a follow up to my previous post … Continue reading

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

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

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The Brown-Erdős-Sós 1973 Conjecture

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

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Three Pictures

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

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

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

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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

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Ilan Karpas: Frankl’s Conjecture for Large Families

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

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

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

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News (mainly polymath related)

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

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A lecture by Noga

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

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