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More Math from Facebook

David Conlon pointed out to two remarkable papers that appeared on the arxive: Joel Moreira solves an old problem in Ramsey’s theory. Monochromatic sums and products in . Abstract: An old question in Ramsey theory asks whether any finite coloring … Continue reading

Posted in Combinatorics, Mathematics over the Internet, Updates | Tagged , , , | 3 Comments

Polymath10-post 4: Back to the drawing board?

It is time for a new polymath10 post on the Erdos-Rado 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

Posted in Combinatorics, Mathematics over the Internet, Polymath10 | 12 Comments

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

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

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 Erdos-Rado 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 , | 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 Erdos-Rado Conjecture and the Erdos-Rado theorem are,  briefly mention some points made in the previous post and in … Continue reading

Posted in Combinatorics, Polymath10 | Tagged , , , | 126 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 Lipton-Tarjan’s theorem extends to high … Continue reading

Posted in Combinatorics, Convex polytopes | Tagged , , , , | 1 Comment

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

Posted in Combinatorics, Number theory | Tagged , | 4 Comments

Updates and plans III.

Update on the great Noga’s Formulas competition. (Link to the original post, many cash prizes are still for grab!) This is the third “Updates and plans post”. The  first one was from 2008 and the  second one from 2011. Updates: Combinatorics and … Continue reading

Posted in Combinatorics, Conferences, Updates | 10 Comments

Combinatorics and More – Greatest Hits

Combinatorics and More’s Greatest Hits First Month Combinatorics, Mathematics, Academics, Polemics, … Helly’s Theorem, “Hypertrees”, and Strange Enumeration I (There were 3 follow up posts:) Extremal Combinatorics I: Extremal Problems on Set Systems (There were 4 follow up posts II ; III; IV; VI) Drachmas Rationality, Economics and … Continue reading

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Greatest Hits

Combinatorics and More’s Greatest Hits First Month Combinatorics, Mathematics, Academics, Polemics, … Helly’s Theorem, “Hypertrees”, and Strange Enumeration I (There were 3 follow up posts:) Extremal Combinatorics I: Extremal Problems on Set Systems (There were 4 follow up posts II ; III; IV; VI) Drachmas Rationality, Economics and … Continue reading

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