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 Alef Corner: Math Collaboration
 Alef’s Corner: Math Collaboration 2
 To cheer you up in difficult times 11: Immortal Songs by Sabine Hossenfelder and by Tom Lehrer
 To cheer you up in difficult times 10: Noam Elkies’ Piano Improvisations and more
 Quantum Matters
 To cheer you up in difficult times 9: Alexey Pokrovskiy proved that Rota’s Basis Conjecture holds asymptotically
 To Cheer you up in Difficult Times 8: Nathan Keller and Ohad Klein Proved Tomaszewski’s Conjecture on Randomly Signed Sums
 Noam Lifshitz: A new hypercontractivity inequality — The proof!
 To cheer you up in difficult times 7: Bloom and Sisask just broke the logarithm barrier for Roth’s theorem!
Top Posts & Pages
 TYI 30: Expected number of Dice throws
 Quantum Matters
 Gil's Collegial Quantum Supremacy Skepticism FAQ
 To Cheer you up in Difficult Times 8: Nathan Keller and Ohad Klein Proved Tomaszewski's Conjecture on Randomly Signed Sums
 Answer: Lord Kelvin, The Age of the Earth, and the Age of the Sun
 A sensation in the morning news  Yaroslav Shitov: Counterexamples to Hedetniemi's conjecture.
 Elchanan Mossel's Amazing Dice Paradox (your answers to TYI 30)
 Hoi Nguyen and Melanie Wood: Remarkable Formulas for the Probability that Projections of Lattices are Surjective
 A Breakthrough by Maryna Viazovska Leading to the Long Awaited Solutions for the Densest Packing Problem in Dimensions 8 and 24
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Monthly Archives: June 2008
The Golden Room and the Golden Mountain
Christine Björner’s words at the Stockholm Festive Combinatorics are now available to all our readers. What makes this moving and interesting, beyond the intimate context of the conference, is our (mathematician’s) struggle (and usually repeated failures) to explain to … Continue reading
Amir Ban on Deep Junior
Ladies and Gentelmen: Amir Ban (right, in the picture above) the guest blogger, was an Israeli Olympiad math champion in the early 70s, with Shay Bushinsky he wrote Deep Junior, and he is also one of the inventors of the “disc on … Continue reading
Euler’s Formula, Fibonacci, the BayerBillera Theorem, and Fine’s CDindex
Bill Gessley proving Euler’s formula (at UMKC) In the earlier post about Billerafest I mentioned the theorem of Bayer and Billera on flag numbers of polytopes. Let me say a little more about it. 1. Euler Euler’s theorem asserts that for … Continue reading
Posted in Combinatorics, Convex polytopes
Tagged BayerBillera's theorem, CDindex, Flag numbers, Jonathan Fine, Lou Billera, Marge Bayer
7 Comments
Helly’s Theorem, “Hypertrees”, and Strange Enumeration II: The Formula
In the first part of this post we discussed an appealing conjecture regaring an extension of Cayley’s counting trees formula. The number of ddimensional “hypertrees” should somehow add up to . But it was not clear to us which complexes we want … Continue reading
Posted in Combinatorics, Convexity
Tagged Cayley theorem, Helly type theorems, Topological combinatorics
6 Comments
Optimism – two quotes
1. Here is a quote from Karl Popper’s paper “Science, Problems, Aims, Responsibilities” about Francis Bacon: “According to Bacon, nature, like God, was present in all things, from the greatest to the least. And it was the aim or the … Continue reading
Billerafest
I am unable to attend the conference taking place now at Cornell, but I send my warmest greetings to Lou from Jerusalem. The titles and abstracts of the lectures can be found here. Let me tell you about two theorems by Lou. … Continue reading
Posted in Conferences, Convex polytopes
Tagged fvectors, flag vectors, gconjecture, Lou Billera
1 Comment
Helly’s Theorem, “Hypertrees”, and Strange Enumeration I
1. Helly’s theorem and Cayley’s formula Helly’s theorem asserts: For a family of n convex sets in , n > d, if every d+1 sets in the family have a point in common then all members in the family have a point in common. … Continue reading
Posted in Combinatorics, Convexity
Tagged Cayley theorem, Helly Theorem, Simplicial complexes, Topological combinatorics, Trees
9 Comments
A Small Debt Regarding Turan’s Problem
Turan’s problem asks for the minimum number of triangles on n vertices so that every 4 vertices span a triangle. (Or equivalently, for the maximum number of triangles on n vertices without a “tetrahedron”, namely without having four triangles on … Continue reading