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# Monthly Archives: March 2009

## An Open Discussion and Polls: Around Roth’s Theorem

Suppose that is a subset of of maximum cardinality not containing an arithmetic progression of length 3. Let . How does behave? We do not really know. Will it help talking about it? Can we somehow look beyond the horizon and try to guess what … Continue reading

Posted in Combinatorics, Open discussion, Open problems
Tagged Cap sets, polymath1, Roth's theorem, Szemeredi's theorem
25 Comments

## A Proposal Regarding Gilad Shalit

Since an agreement for the release of Gilad Shalit in exchange for the release of Hamas prisoners could not be reached, I propose to initiate negotiations (perhaps with Egyptian help) on the improvement of Gilad Shalit’s captivity conditions. In return … Continue reading

## A Deeper Look at Basketball

This basketball is combinatorially equivalent to? Answer

## Colorful Caratheodory Revisited

Janos Pach wrote me: “I saw that you several times returned to the colored Caratheodory and Helly theorems and related stuff, so I thought that you may be interested in the enclosed paper by Holmsen, Tverberg and me, in … Continue reading

## A Beautiful Garden of Hypertrees

We had a series of posts (1,2,3,4) “from Helly to Cayley” on weighted enumeration of Q-acyclic simplicial complexes. The simplest case beyond Cayley’s theorem were Q-acyclic complexes with vertices, edges, and triangles. One example is the six-vertex triangulation of the … Continue reading

Posted in Combinatorics
Tagged Mishael Rosenthal, Nati Linial, Roy Meshulam, Topological combinatorics, Trees
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## Extremal Combinatorics on Permutations

We talked about extremal problems for set systems: collections of subsets of an element sets, – Sperner’s theorem, the Erdos-Ko-Rado theorem, and quite a few more. (See here, here and here.) What happens when we consider collections of permutations rather … Continue reading

Posted in Combinatorics
Tagged Erdos-Ko-Rado theorem, Extremal combinatorics, Permutations
9 Comments

## Polymath1: Success!

“polymath” based on internet image search And here is a link to the current draft of the paper. Update: March 26, the name of the post originally entitled “Polymath1: Probable Success!” was now updated to “Polymath1: Success!” It is now becoming … Continue reading

Posted in Blogging, Combinatorics, What is Mathematics
Tagged Density Hales-Jewett theorem, polymath1
10 Comments

## Do Politicians Act Rationally?

Well, I wrote an article (in Hebrew) about it in the Newspaper Haaretz. An English translation appeared in the English edition. Here is an appetizer: During World War II, many fighter planes returned from bombing missions in Japan full of bullet holes. The … Continue reading

## Noise Sensitivity Lecture and Tales

A lecture about Noise sensitivity Several of my recent research projects are related to noise, and noise was also a topic of a recent somewhat philosophical post. My oldest and perhaps most respectable noise-related project was the work with Itai Benjamini and Oded … Continue reading

## The Mystery Beeping Riddle

We came back from the airport with our daughter who has just landed after a four-month trip to India. The car was making a strange beep every so often. Maybe it is an indicator signal that should have … Continue reading

Posted in Mathematics to the rescue, Rationality, Riddles
12 Comments