Tag Archives: Peter Frankl

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

Posted on March 9, 2018 by

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 , , , | 12 Comments

Hardness of Approximating Vertex Cover, Polytope-Integrality-Gap, the Alswede-Kachatrian theorem, and More.

Posted on January 21, 2018 by

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 →

Posted in Combinatorics, Computer Science and Optimization | Tagged , , , , , , , | 1 Comment

Ilan Karpas: Frankl’s Conjecture for Large Families

Posted on December 26, 2017 by

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 →

Posted in Combinatorics, Open problems | Tagged , , , | 3 Comments

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

Posted on December 10, 2017 by

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

News (mainly polymath related)

Posted on January 20, 2016 by

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 →

Posted in Combinatorics, Conferences, Mathematics over the Internet, Polymath10, Polymath3, Updates | Tagged , , , , , , , | 11 Comments

A lecture by Noga

Posted on October 9, 2014 by

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 →

Posted in Combinatorics, Conferences | Tagged , , , , , , | Leave a comment

Extremal Combinatorics VI: The Frankl-Wilson Theorem

Posted on May 21, 2009 by

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 →

Posted in Combinatorics | Tagged , | 18 Comments

Combinatorics, Mathematics, Academics, Polemics, …

Posted on April 29, 2008 by

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 →

Posted in Blogging, Combinatorics, Controversies and debates, Open problems | Tagged , , , , , , , , , , , | 19 Comments