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Category Archives: Combinatorics
Polymath10post 4: Back to the drawing board?
It is time for a new polymath10 post on the ErdosRado Sunflower Conjecture. (Here are the links for post1, post2, post3.) Let me summarize the discussion from Post 3 and we can discuss together what directions to peruse. It is … Continue reading
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
Polymath 10 Post 3: How are we doing?
The main purpose of this post is to start a new research thread for Polymath 10 dealing with the ErdosRado Sunflower problem. (Here are links to post 2 and post 1.) Here is a very quick review of where we … Continue reading
Posted in Combinatorics, Mathematics over the Internet, Open problems, Polymath10
Tagged polymath10, sunflower conjecture
104 Comments
Polymath10, Post 2: Homological Approach
We launched polymath10 a week ago and it is time for the second post. In this post I will remind the readers what the ErdosRado Conjecture and the ErdosRado theorem are, briefly mention some points made in the previous post and in … Continue reading
Polymath10: The Erdos Rado Delta System Conjecture
The purpose of this post is to start the polymath10 project. It is one of the nine projects (project 3d) proposed by Tim Gowers in his post “possible future polymath projects”. The plan is to attack ErdosRado delta system conjecture also known as the … Continue reading
Posted in Combinatorics, Polymath10
Tagged Alexandr Kostochka, Joel Spencer, Paul Erdos, Richard Rado
139 Comments
Convex Polytopes: Seperation, Expansion, Chordality, and Approximations of Smooth Bodies
I am happy to report on two beautiful results on convex polytopes. One disproves an old conjecture of mine and one proves an old conjecture of mine. Loiskekoski and Ziegler: Simple polytopes without small separators. Does LiptonTarjan’s theorem extends to high … Continue reading
Igor Pak’s collection of combinatorics videos
The purpose of this short but valuable post is to bring to your attention Igor Pak’s Collection of Combinatorics Videos
EDP Reflections and Celebrations
The Problem In 1932, Erdős conjectured: Erdős Discrepancy Conjecture (EDC) [Problem 9 here] For any constant , there is an such that the following holds. For any function , there exists an and a such that For any , … Continue reading
Séminaire N. Bourbaki – Designs Exist (after Peter Keevash) – the paper
Update: Nov 4, 2015: Here is the final version of the paper: Design exists (after P. Keevash). On June I gave a lecture on Bourbaki’s seminare devoted to Keevash’s breakthrough result on the existence of designs. Here is a draft of the … Continue reading
Important formulas in Combinatorics
Another spinoff of the Nogaposterformulacompetition is a MathOverflow question: Important formulas in combinatorics. The question collects important formulas representing major progress in combinatorics. So far there are 31 formulas and quite a few were new to me. There are several areas … Continue reading