Monthly Archives: March 2009

An Open Discussion and Polls: Around Roth’s Theorem

Posted on March 25, 2009 by Gil Kalai

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 , , , | 31 Comments

A Proposal Regarding Gilad Shalit

Posted on March 24, 2009 by Gil Kalai

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 →

Posted in Uncategorized | Tagged | 9 Comments

A Deeper Look at Basketball

Posted on March 21, 2009 by Gil Kalai

This basketball is combinatorially equivalent to? Answer

Posted in Sport | Tagged | 18 Comments

Colorful Caratheodory Revisited

Posted on March 15, 2009 by Gil Kalai

  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 →

Posted in Convexity | Tagged | 3 Comments

A Beautiful Garden of Hypertrees

Posted on March 14, 2009 by Gil Kalai

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 , , , , | 2 Comments

Extremal Combinatorics on Permutations

Posted on March 13, 2009 by Gil Kalai

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 than … Continue reading →

Posted in Combinatorics | Tagged , , , , , | 10 Comments

Polymath1: Success!

Posted on March 11, 2009 by Gil Kalai

“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 , , | 10 Comments

Do Politicians Act Rationally?

Posted on March 9, 2009 by Gil Kalai

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 →

Posted in Games, Rationality | Tagged , , , , | 4 Comments

Noise Sensitivity Lecture and Tales

Posted on March 6, 2009 by Gil Kalai

  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 →

Posted in Combinatorics, Computer Science and Optimization, Probability | Tagged , , , , , , | 14 Comments

The Mystery Beeping Riddle

Posted on March 3, 2009 by Gil Kalai

    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