Monthly Archives: June 2011

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 | 8 Comments

The Combinatorics of Cocycles and Borsuk’s Problem.

Cocycles Definition:  A -cocycle is a collection of -subsets such that every -set contains an even number of sets in the collection. Alternative definition: Start with a collection of -sets and consider all -sets that contain an odd number of members … Continue reading

Posted in Combinatorics, Convexity, Open problems | Tagged , , , , | 2 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, here … Continue reading

Posted in Updates | Tagged , , , | 6 Comments

Another way to Revolutionize Football

The angle of Victoria Beckham’s hat (here in a picture from a recent wedding) is closely related to our previous post on football One of the highlights of the recent Newton Institute  conference on discrete harmonic analysis was a football … Continue reading

Posted in Games, Mathematics to the rescue, Sport | Tagged , | 8 Comments