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Category Archives: Combinatorics
Cohen, Haeupler, and Schulman: Explicit Binary Tree-Codes & Cancellations
The high-dimensional conference in Jerusalem is running with many exciting talks (and they are videotaped), and today in Tel Aviv there is a conference on Optimization and Discrete Geometry : Theory and Practice. Today in Jerusalem, Leonard Schulman talked (video available!) … Continue reading
Test Your Intuition (34): Tiling high dimensional spaces with two-dimensional tiles.
A tile is a finite subset of . We can ask if can or cannot be partitioned into copies of . If can be partitioned into copies of we say that tiles . Here is a simpe example. Let consists of … Continue reading
Coloring Problems for Arrangements of Circles (and Pseudocircles)
To supplement and celebrate Aubrey de Grey’s result here are Eight problems on coloring circles A) Consider a finite family of unit circles. What is the minimum number of colors needed to color the circles so that tangent circles are … Continue reading
Posted in Combinatorics, Geometry, Open problems
Tagged Geometric combinatorics, geometric graphs, Graph-coloring
8 Comments
Aubrey de Grey: The chromatic number of the plane is at least 5
A major progress on an old standing beautiful problem. Aubrey de Grey proved that the chromatic number of the plane is at least 5. (I first heard about it from Alon Amit.) The Hadwiger–Nelson problem asks for the minimum number of … Continue reading
Posted in Combinatorics, Geometry, Open problems, Updates
Tagged Aubrey de Grey, The Hadwiger–Nelson problem
10 Comments
Conference on High Dimensional Combinatorics, April 22-26 2018
Conference on High Dimensional Combinatorics Conference home-page Dates: April 22-26, 2018 Place: Israel Institute for Advanced Studies, The Hebrew University of Jerusalem Organizers: Alex Lubotzky, Tali Kaufman and Oren Becker Registration form: click here Registration deadline: April 13, 2018 Combinatorics in general and the theory … Continue reading
Nathan Rubin Improved the Bound for Planar Weak ε-Nets and Other News From Ein-Gedi
I just came back from a splendid visit to Singapore and Vietnam and I will write about it later. While I was away, Nathan Rubin organized a lovely conference on topics closed to my heart ERC Workshop: Geometric Transversals and Epsilon-Nets with … Continue reading
A Wonderful Paper by Igor Pak: Complexity Problems in Enumerative Combinatorics
Greetings from Sa Pa in the very north of Vietnam. Let me recommend a great thought-provoking paper by Igor Pak: Complexity problems in enumerative combinatorics. As Igor wrote on his blog: Well, I finally finished my ICM paper. It’s only 30 … Continue reading
Frankl’s Conjecture for Large Families: Ilan Karpas’ Proof
Frankl’s conjecture asserts that a for every finite family of of finite sets that is closed under union, there is an element that belongs to at least half the sets in the family. We mentioned the problem in our very … Continue reading
Test your intuition 33: Why is the density of any packing of unit balls decay exponentially with the dimension?
Test your intuition: What is the simplest explanation you can give to the fact that the density of every packing of unit balls in is exponentially small in ? Answers are most welcome. Of course, understanding the asymptotic behavior of … Continue reading
Posted in Combinatorics, Geometry, Test your intuition
Tagged Serge Vlăduţ, Sphere packing
4 Comments
Serge Vlăduţ : Lattices with exponentially large kissing numbers
(I thank Avi Wigderson for telling me about it.) Serge Vlăduţ just arxived a paper with examples of lattices in such that the kissing number is exponential in . The existence of such a lattice is a very old open … Continue reading
