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- Joshua Hinman proved Bárány’s conjecture on face numbers of polytopes, and Lei Xue proved a lower bound conjecture by Grünbaum.
- Amazing: Jinyoung Park and Huy Tuan Pham settled the expectation threshold conjecture!
- Combinatorial Convexity: A Wonderful New Book by Imre Bárány
- Chaim Even-Zohar, Tsviqa Lakrec, and Ran Tessler present: The Amplituhedron BCFW Triangulation
- Ehud Friedgut: How many cubes of 2×2×2 fit into a box of size 8×4×3? (TYI 49)
- Is HQCA Possible? A conversation with Michael Brooks
- To cheer you up in difficult times 35 combined with Test Your Intuition 48: Alef’s corner – Jazz and Math
- Reflections: On the Occasion of Ron Adin’s and Yuval Roichman’s Birthdays, and FPSAC 2021
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- Amazing: Jinyoung Park and Huy Tuan Pham settled the expectation threshold conjecture!
- Joshua Hinman proved Bárány's conjecture on face numbers of polytopes, and Lei Xue proved a lower bound conjecture by Grünbaum.
- TYI 30: Expected number of Dice throws
- Game Theory 2021
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- Telling a Simple Polytope From its Graph
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- Answer: Lord Kelvin, The Age of the Earth, and the Age of the Sun
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Tag Archives: Cap sets
Mind Boggling: Following the work of Croot, Lev, and Pach, Jordan Ellenberg settled the cap set problem!
A quote from a recent post from Jordan Ellenberg‘s blog Quomodocumque: Briefly: it seems to me that the idea of the Croot-Lev-Pach paper I posted about yesterday (GK: see also my last post) can indeed be used to give a new bound … Continue reading
Posted in Combinatorics, Open problems, Updates
Tagged Cap sets, Dion Gijswijt, Ernie Croot, Jordan Ellenberg, Peter Pach, Seva Lev.
25 Comments
Cap 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 Group-theoretic algorithms for matrix multiplication, by Henry Cohn, Robert Kleinberg, Balasz Szegedy, and Christopher Umans (CKSU05), … Continue reading
The Cap-Set Problem and Frankl-Rodl Theorem (C)
Update: This is a third of three posts (part I, part II) proposing some extensions of the cap set problem and some connections with the Frankl Rodl theorem. Here is a post presenting the problem on Terry Tao’s blog (March 2007). Here … Continue reading
Around the Cap-Set problem (B)
Part B: Finding special cap sets This is a second part in a 3-part 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
Frankl-Rodl’s Theorem and Variations on the Cap Set Problem: A Recent Research Project with Roy Meshulam (A)
Voita Rodl I would like to tell you about a research project in progress with Roy Meshulam. (We started it in the summer, but then moved to other things; so far there are interesting insights, and perhaps problems, but not substantial … Continue reading
Posted in Combinatorics, Open problems
Tagged Cap sets, Extremal combinatorics, Intersection theorems, polymath1
10 Comments