- Amazing: Stefan Glock, Daniela Kühn, Allan Lo, and Deryk Osthus give a new proof for Keevash’s Theorem. And more news on designs.
- The US Elections and Nate Silver: Informtion Aggregation, Noise Sensitivity, HEX, and Quantum Elections.
- Avifest live streaming
- AlexFest: 60 Faces of Groups
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- AviFest, AviStories and Amazing Cash Prizes.
- Polymath 10 post 6: The Erdos-Rado sunflower conjecture, and the Turan (4,3) problem: homological approaches.
- Polymath 10 Emergency Post 5: The Erdos-Szemeredi Sunflower Conjecture is Now Proven.
Top Posts & Pages
- Answer: Lord Kelvin, The Age of the Earth, and the Age of the Sun
- Amazing: Stefan Glock, Daniela Kühn, Allan Lo, and Deryk Osthus give a new proof for Keevash's Theorem. And more news on designs.
- יופיה של המתמטיקה
- Sarkaria's Proof of Tverberg's Theorem 1
- The Quantum Computer Puzzle @ Notices of the AMS
- Emmanuel Abbe: Erdal Arıkan's Polar Codes
- Believing that the Earth is Round When it Matters
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- A Breakthrough by Maryna Viazovska Leading to the Long Awaited Solutions for the Densest Packing Problem in Dimensions 8 and 24
Tag Archives: Topological combinatorics
We launched polymath10 a week ago and it is time for the second post. In this post I will remind the readers what the Erdos-Rado Conjecture and the Erdos-Rado theorem are, briefly mention some points made in the previous post and in … Continue reading
This is a new polymath3 research thread. Our aim is to tackle the polynomial Hirsch conjecture which asserts that there is a polynomial upper bound for the diameter of graphs of -dimensional polytopes with facets. Our research so far was … Continue reading
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
In the first part of this post we discussed an appealing conjecture regaring an extension of Cayley’s counting trees formula. The number of d-dimensional “hypertrees” should somehow add up to . But it was not clear to us which complexes we want … Continue reading
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
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