Recent Comments

Recent Posts
 In And Around Combinatorics: The 18th Midrasha Mathematicae. Jerusalem, JANUARY 1831
 Mathematical Gymnastics
 Media Item from “Haaretz” Today: “For the first time ever…”
 Jim Geelen, Bert Gerards, and Geoﬀ Whittle Solved Rota’s Conjecture on Matroids
 Media items on David, Amnon, and Nathan
 Next Week in Jerusalem: Special Day on Quantum PCP, Quantum Codes, Simplicial Complexes and Locally Testable Codes
 Happy Birthday Ervin, János, Péter, and Zoli!
 My Mathematical Dialogue with Jürgen Eckhoff
 Test Your Intuition (23): How Many Women?
Top Posts & Pages
 In And Around Combinatorics: The 18th Midrasha Mathematicae. Jerusalem, JANUARY 1831
 Believing that the Earth is Round When it Matters
 The Intermediate Value Theorem Applied to Football
 János Pach: Guth and Katz's Solution of Erdős's Distinct Distances Problem
 Answer: Lord Kelvin, The Age of the Earth, and the Age of the Sun
 About
 Polymath 8  a Success!
 In how many ways you can chose a committee of three students from a class of ten students?
 The KadisonSinger Conjecture has beed Proved by Adam Marcus, Dan Spielman, and Nikhil Srivastava
RSS
Category Archives: Open problems
How Large can a Spherical Set Without Two Orthogonal Vectors Be?
The problem Problem: Let be a measurable subset of the dimensional sphere . Suppose that does not contain two orthogonal vectors. How large can the dimensional volume of be? A Conjecture Conjecture: The maximum volume is attained by two … Continue reading
Posted in Open problems
4 Comments
The CapSet Problem and FranklRodl 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
Posted in Combinatorics, Open problems
Tagged Cap sets, FranklRodl theorem, polymath1
Leave a comment
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
A Problem on Planar Percolation
Conjecture (Gady Kozma): Prove that the critical probability for planar percolation on a Cayley graph of the group is always an algebraic number. Gady mentioned this conjecture in his talk here about percolation on infinite Cayley graphs. (Update April 30: Today Gady mentioned … Continue reading
(Eran Nevo) The gConjecture II: The Commutative Algebra Connection
Richard Stanley This post is authored by Eran Nevo. (It is the second in a series of five posts.) The gconjecture: the commutative algebra connection Let be a triangulation of a dimensional sphere. Stanley’s idea was to associate with a ring … Continue reading
How the gConjecture Came About
This post complements Eran Nevo’s first post on the conjecture 1) Euler’s theorem Euler Euler’s famous formula for the numbers of vertices, edges and faces of a polytope in space is the starting point of many mathematical stories. (Descartes came close … Continue reading
(Eran Nevo) The gConjecture I
This post is authored by Eran Nevo. (It is the first in a series of five posts.) Peter McMullen The gconjecture What are the possible face numbers of triangulations of spheres? There is only one zerodimensional sphere and it consists … Continue reading
Posted in Combinatorics, Convex polytopes, Guest blogger, Open problems
Tagged face rings, gconjecture, Polytopes
5 Comments
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
25 Comments
Rosenfeld’s OddDistance Problem
Moshe Rosenfeld’s odddistance problem: Let G be the graph whose vertices are points in the plane and two vertices form an edge if their distance is an odd integer. Is the chromatic number of this graph finite?
Posted in Combinatorics, Open problems
1 Comment
FranklRodl’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
6 Comments