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 Reflections: On the Occasion of Ron Adin’s and Yuval Roichman’s Birthdays, and FPSAC 2021
 ICM 2018 Rio (5) Assaf Naor, Geordie Williamson and Christian Lubich
 Test your intuition 47: AGCGTCTGCGTCTGCGACGATC? what comes next in the sequence?
 Cheerful news in difficult times: Richard Stanley wins the Steele Prize for lifetime achievement!
 Combinatorial Theory is Born
 To cheer you up in difficult times 34: Ringel Circle Problem solved by James Davies, Chaya Keller, Linda Kleist, Shakhar Smorodinsky, and Bartosz Walczak
 Good Codes papers are on the arXiv
 To cheer you up in difficult times 33: Deep learning leads to progress in knot theory and on the conjecture that KazhdanLusztig polynomials are combinatorial.
 The Logarithmic Minkowski Problem
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 NavierStokes Fluid Computers
 The Intermediate Value Theorem Applied to Football
 TYI 30: Expected number of Dice throws
 Believing that the Earth is Round When it Matters
 To Cheer You Up in Difficult Times 31: Federico Ardila's Four Axioms for Cultivating Diversity
 Amazing: Karim Adiprasito proved the gconjecture for spheres!
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 To cheer you up in difficult times 27: A major recent "Lean" proof verification
 Happy Birthday Richard Stanley!
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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
11 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
29 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
14 Comments