Search Results for: erdos

Cup Sets, Sunflowers, and Matrix Multiplication

This post follows a recent paper On sunflowers  and matrix multiplication by Noga Alon, Amir Spilka, and Christopher Umens (ASU11) which rely on an earlier paper Group-theoretic algorithms for matrix multiplication, by Henry Cohn, Robert Kleinberg, Balasz Szegedy, and Christopher Umans (CKSU05), … Continue reading

Posted in Combinatorics, Computer Science and Optimization, Open problems | Tagged , , , , , , | 3 Comments

Discrepancy, The Beck-Fiala Theorem, and the Answer to “Test Your Intuition (14)”

The Question Suppose that you want to send a message so that it will reach all vertices of the discrete -dimensional cube. At each time unit (or round) you can send the message to one vertex. When a vertex gets the … Continue reading

Posted in Combinatorics, Test your intuition | Tagged , | 6 Comments

Around Borsuk’s Conjecture 1: Some Problems

Greetings to all! Karol Borsuk conjectured in 1933 that every bounded set in can be covered by sets of smaller diameter. In a previous post I described the counterexample found by Jeff Kahn and me. I will devote a few posts … Continue reading

Posted in Combinatorics, Convexity | Tagged | 7 Comments

Tentative Plans and Belated Updates II

  Elementary school reunion: Usually, I don’t write about personal matters over the blog, but having (a few weeks ago) an elementary school reunion after 42 years was a moving and exciting event as to consider making an exception. For now, … Continue reading

Posted in Updates | Tagged , , , | 6 Comments

Polymath Reflections

Polymath is a collective open way of doing mathematics. It  started over Gowers’s blog with the polymath1 project that was devoted to the Density Hales Jewett problem. Since then we  had Polymath2 related to Tsirelson spaces in Banach space theory , an  intensive Polymath4 devoted … Continue reading

Posted in Mathematics over the Internet, Open discussion | 2 Comments

A Discrepancy Problem for Planar Configurations

Yaacov Kupitz and Micha A. Perles asked: What is the smallest number C such that for every configuration of n points in the plane there is a line containing two or more points from the configuration for which the difference between the … Continue reading

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Polymath5 – Is 2 logarithmic in 1124?

 Polymath5 – The Erdős discrepancy problem – is on its way. Update (September 2015): Terry Tao have now solved Erdos discrepancy problem and proved that indeed the discrepancy tends to infinity. See also this blog post on Tao’s blog. Update: Gowers’s … Continue reading

Posted in Mathematics over the Internet | Tagged | 3 Comments

Four Derandomization Problems

Polymath4 is devoted to a question about derandomization: To find a deterministic polynomial time algorithm for finding a k-digit prime.  So I (belatedly) devote this post to derandomization and, in particular, the following four problems. 1) Find a deterministic algorithm for primality 2) Find … Continue reading

Posted in Computer Science and Optimization, Probability | Tagged , , | 5 Comments

Vitali Fest

Last week I took part in a lovely and impressive conference on the state of geometry and functional analysis, celebrating Vitali Milman’s 70th birthday. The conference started in Tel Aviv, continued at the Dead Sea, and returned to Tel Aviv. I gave a … Continue reading

Posted in Conferences | 5 Comments

The Cap-Set Problem and Frankl-Rodl Theorem (C)

Update: This is a third of three posts (part I, part II) proposing some extensions of the cap set problem and some connections with the Frankl Rodl theorem. Here is a post presenting the problem on Terry Tao’s blog (March 2007). Here … Continue reading

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