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 Jacob Fox, David Conlon, and Benny Sudakov: Vast Improvement of our Knowledge on Unavoidable Patterns in Words
 Subhash Khot, Dor Minzer and Muli Safra proved the 2to2 Games Conjecture
 Interesting Times in Mathematics: Enumeration Without Numbers, Group Theory Without Groups.
 Cody Murray and Ryan Williams’ new ACC breakthrough: Updates from Oded Goldreich’s Choices
 Yael Tauman Kalai’s ICM2018 Paper, My Paper, and Cryptography
 Ilan Karpas: Frankl’s Conjecture for Large Families
 Third third of my ICM 2018 paper – Three Puzzles on Mathematics, Computation and Games. Corrections and comments welcome
 Second third of my ICM 2018 paper – Three Puzzles on Mathematics, Computation and Games. Corrections and comments welcome
 First third of my ICM2018 paper – Three Puzzles on Mathematics, Computation and Games. Corrections and comments welcome
Top Posts & Pages
 Jacob Fox, David Conlon, and Benny Sudakov: Vast Improvement of our Knowledge on Unavoidable Patterns in Words
 Subhash Khot, Dor Minzer and Muli Safra proved the 2to2 Games Conjecture
 Answer: Lord Kelvin, The Age of the Earth, and the Age of the Sun
 Interesting Times in Mathematics: Enumeration Without Numbers, Group Theory Without Groups.
 Cody Murray and Ryan Williams' new ACC breakthrough: Updates from Oded Goldreich's Choices
 Elchanan Mossel's Amazing Dice Paradox (your answers to TYI 30)
 Yael Tauman Kalai's ICM2018 Paper, My Paper, and Cryptography
 If Quantum Computers are not Possible Why are Classical Computers Possible?
 TYI 30: Expected number of Dice throws
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Tag Archives: Roth’s theorem
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
4 Comments
Roth’s Theorem: Tom Sanders Reaches the Logarithmic Barrier
Click here for the most recent polymath3 research thread. I missed Tom by a few minutes at MittagLeffler Institute a year and a half ago Suppose that is a subset of of maximum cardinality not containing an arithmetic progression of length 3. Let . … Continue reading
Posted in Combinatorics, Open problems
Tagged Endre Szemeredi, Jean Bourgain, Klaus Roth, Roger HeathBrown, Roth's theorem, Tom Sanders
9 Comments
Around the CapSet problem (B)
Part B: Finding special cap sets This is a second part in a 3part series about variations on the cap set problem that I studied with Roy Meshulam. (The first post is here.) I will use here a different notation than in part … Continue reading
An Open Discussion and Polls: Around Roth’s Theorem
Suppose that is a subset of of maximum cardinality not containing an arithmetic progression of length 3. Let . How does behave? We do not really know. Will it help talking about it? Can we somehow look beyond the horizon and try to guess what … Continue reading
Posted in Combinatorics, Open discussion, Open problems
Tagged Cap sets, polymath1, Roth's theorem, Szemeredi's theorem
26 Comments
Pushing Behrend Around
Erdos and Turan asked in 1936: What is the largest subset of {1,2,…,n} without a 3term arithmetic progression? In 1946 Behrend found an example with Now, sixty years later, Michael Elkin pushed the the factor from the denominator to the enumerator, … Continue reading
Posted in Combinatorics, Updates
Tagged Arithmetic progressions, Roth's theorem, Szemeredi's theorem
10 Comments