- My Very First Book “Gina Says”, Now Published by “World Scientific”
- Itai Benjamini: Coarse Uniformization and Percolation & A Paper by Itai and me in Honor of Lucio Russo
- After-Dinner Speech for Alex Lubotzky
- Boaz Barak: The different forms of quantum computing skepticism
- Bálint Virág: Random matrices for Russ
- Test Your Intuition 33: The Great Free Will Poll
- Must-read book by Avi Wigderson
- High Dimensional Combinatorics at the IIAS – Program Starts this Week; My course on Helly-type theorems; A workshop in Sde Boker
- Stan Wagon, TYI 23: Ladies and Gentlemen: The Answer
Top Posts & Pages
- My Very First Book "Gina Says", Now Published by "World Scientific"
- Elchanan Mossel's Amazing Dice Paradox (your answers to TYI 30)
- TYI 30: Expected number of Dice throws
- Why Quantum Computers Cannot Work: The Movie!
- The Race to Quantum Technologies and Quantum Computers (Useful Links)
- Answer: Lord Kelvin, The Age of the Earth, and the Age of the Sun
- Amazing: Peter Keevash Constructed General Steiner Systems and Designs
- If Quantum Computers are not Possible Why are Classical Computers Possible?
Tag Archives: Borsuk’s conjecture
Borsuk asked in 1933 if every bounded set K of diameter 1 in can be covered by d+1 sets of smaller diameter. A positive answer was referred to as the “Borsuk Conjecture,” and it was disproved by Jeff Kahn and me in 1993. … Continue reading
The news in brief Andriy V. Bondarenko proved in his remarkable paper The Borsuk Conjecture for two-distance sets that the Borsuk’s conjecture is false for all dimensions greater than 65. This is a substantial improvement of the earlier record (all dimensions … Continue reading
Problem: Let P be a polytope in with n facets. Is it always true that P can be covered by n sets of smaller diameter? I also asked this question over mathoverflow, with some background and motivation.
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
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
Andrei Raigorodskii (This post follows an email by Aicke Hinrichs.) In a previous post we discussed the following problem: Problem: Let be a measurable subset of the -dimensional sphere . Suppose that does not contain two orthogonal vectors. How large … Continue reading
Jeff Kahn Jeff and I worked on the problem for several years. Once he visited me with his family for two weeks. Before the visit I emailed him and asked: What should we work on in your visit? Jeff asnwered: … Continue reading