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 Polymath 10 post 6: The ErdosRado sunflower conjecture, and the Turan (4,3) problem: homological approaches.
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Category Archives: Open problems
Octonions to the Rescue
Xavier Dahan and JeanPierre Tillich’s Octonionbased Ramanujan Graphs with High Girth. Update (February 2012): Non associative computations can be trickier than we expect. Unfortunately, the paper by Dahan and Tillich turned out to be incorrect. Update: There is more to … Continue reading
The SimonovitsSos Conjecture was Proved by Ellis, Filmus and Friedgut
Simonovits and Sos asked: Let be a family of graphs with N={1,2,…,n} as the set of vertices. Suppose that every two graphs in the family have a triangle in common. How large can be? (We talked about it in this post.) … Continue reading
Posted in Combinatorics, Open problems
10 Comments
Polymath3: Polynomial Hirsch Conjecture 4
So where are we? I guess we are trying all sorts of things, and perhaps we should try even more things. I find it very difficult to choose the more promising ideas, directions and comments as Tim Gowers and Terry Tao did so … Continue reading
Posted in Combinatorics, Convex polytopes, Open discussion, Open problems, Polymath3
Tagged Hirsch conjecture, Polymath3
73 Comments
Polymath3 : Polynomial Hirsch Conjecture 3
Here is the third research thread for the polynomial Hirsch conjecture. I hope that people will feel as comfortable as possible to offer ideas about the problem we discuss. Even more important, to think about the problem either in the directions suggested by … Continue reading
Posted in Combinatorics, Convex polytopes, Open discussion, Open problems, Polymath3
Tagged Polymath3
102 Comments
Polymath 3: The Polynomial Hirsch Conjecture 2
Here we start the second research thread about the polynomial Hirsch conjecture. I hope that people will feel as comfortable as possible to offer ideas about the problem. The combinatorial problem looks simple and also everything that we know about it is rather simple: … Continue reading
Posted in Convex polytopes, Open discussion, Open problems, Polymath3
Tagged Hirsch conjecture, Polymath3
104 Comments
Polymath 3: Polynomial Hirsch Conjecture
I would like to start here a research thread of the longpromised Polymath3 on the polynomial Hirsch conjecture. I propose to try to solve the following purely combinatorial problem. Consider t disjoint families of subsets of {1,2,…,n}, . Suppose that … Continue reading
Posted in Convex polytopes, Open discussion, Open problems, Polymath3
Tagged Hirsch conjecture, Polymath3
119 Comments
The Polynomial Hirsch Conjecture: The Crux of the Matter.
Consider t disjoint families of subsets of {1,2,…,n}, . Suppose that (*) For every , and every and , there is which contains . The basic question is: How large can t be??? Let’s call the answer f(n). … Continue reading
Posted in Combinatorics, Convex polytopes, Open problems, Polymath3
5 Comments
Francisco Santos Disproves the Hirsch Conjecture
A title and an abstract for the conference “100 Years in Seattle: the mathematics of Klee and Grünbaum” drew a special attention: Title: “A counterexample to the Hirsch conjecture” Author: Francisco Santos, Universidad de Cantabria Abstract: I have been in … Continue reading
Posted in Convex polytopes, Open problems, Polymath3
36 Comments
The Polynomial Hirsch Conjecture: Discussion Thread, Continued
Here is a link for the justposted paper Diameter of Polyhedra: The Limits of Abstraction by Freidrich Eisenbrand, Nicolai Hahnle, Sasha Razborov, and Thomas Rothvoss. And here is a link to the paper by Sandeep Koranne and Anand Kulkarni “The dstep Conjecture is Almost true” – … Continue reading
Posted in Convex polytopes, Open discussion, Open problems
Tagged Convex polytopes, Hirsch conjecture
16 Comments
(Eran Nevo) The gConjecture III: Algebraic Shifting
This is the third in a series of posts by Eran Nevo on the gconjecture. Eran’s first post was devoted to the combinatorics of the gconjecture and was followed by a further post by me on the origin of the gconjecture. … Continue reading
Posted in Combinatorics, Convex polytopes, Guest blogger, Open problems
Tagged gconjecture, Shifting
3 Comments