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 Combinatorics and More – Greatest Hits
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 The Simplex, the Cyclic polytope, the Positroidron, the Amplituhedron, and Beyond
 From Oberwolfach: The Topological Tverberg Conjecture is False
 Midrasha Mathematicae #18: In And Around Combinatorics
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 The AC0 Prime Number Conjecture
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 From Oberwolfach: The Topological Tverberg Conjecture is False
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Category Archives: Combinatorics
Ryan O’Donnell: Analysis of Boolean Function
Ryan O’Donnell has begun writing a book about Fourier analysis of Boolean functions and he serializes it on a blog entiled Analysis of Boolean Function. New sections appear on Mondays, Wednesdays, and Fridays. Besides covering the basic theory, Ryan intends to describe applications … Continue reading
Cup Sets, Sunflowers, and Matrix Multiplication
This post follows a recent paper On sunflowers and matrix multiplication by Noga Alon, Amir Spilka, and Christopher Umens (ASU11) which rely on an earlier paper Grouptheoretic algorithms for matrix multiplication, by Henry Cohn, Robert Kleinberg, Balasz Szegedy, and Christopher Umans (CKSU05), … Continue reading
High Dimensional Expanders: Introduction I
Alex Lubotzky and I are running together a year long course at HU on High Dimensional Expanders. High dimensional expanders are simplical (and more general) cell complexes which generalize expander graphs. The course is taking place in Room 110 of the mathematics building on … Continue reading
Posted in Combinatorics, Teaching
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Noise Sensitivity and Percolation. Lecture Notes by Christophe Garban and Jeff Steif
Lectures on noise sensitivity and percolation is a new beautiful monograph by Christophe Garban and Jeff Steif. (Some related posts on this blog: 1, 2, 3, 4, 5)
Posted in Combinatorics, Probability
Tagged Christoph Garban, Jeff Steif, Noise, Noisesensitivity, Percolation
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Alantha Newman and Alexandar Nikolov Disprove Beck’s 3Permutations Conjecture
Alantha Newman and Alexandar Nikolov disproved a few months ago one of the most famous and frustrating open problem in discrepancy theory: Beck’s 3permutations conjecture. Their paper A counterexample to Beck’s conjecture on the discrepancy of three permutations is already on … Continue reading
Discrepancy, The BeckFiala Theorem, and the Answer to “Test Your Intuition (14)”
The Question Suppose that you want to send a message so that it will reach all vertices of the discrete dimensional cube. At each time unit (or round) you can send the message to one vertex. When a vertex gets the … Continue reading
Test Your Intuition (14): A Discrete Transmission Problem
Recall that the dimensional discrete cube is the set of all binary vectors ( vectors) of length n. We say that two binary vectors are adjacent if they differ in precisely one coordinate. (In other words, their Hamming distance is 1.) This … Continue reading
A Couple Updates on the AdvancesinCombinatorics Updates
In a recent post I mentioned quite a few remarkable recent developments in combinatorics. Let me mention a couple more. Independent sets in regular graphs A challenging conjecture by Noga Alon and Jeff Kahn in graph theory was about the number of … Continue reading
Posted in Combinatorics, Open problems, Updates
Tagged Independent sets in graphs, Roth's theorem
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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
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