Recent Comments

Recent Posts
 Friendship and Sesame, Maryam and Marina, Israel and Iran
 Elchanan Mossel’s Amazing Dice Paradox (your answers to TYI 30)
 TYI 30: Expected number of Dice throws
 Test your intuition 29: Diameter of various random trees
 Micha Perles’ Geometric Proof of the ErdosSos Conjecture for Caterpillars
 Touching Simplices and Polytopes: Perles’ argument
 Where were we?
 Call for nominations for the Ostrowski Prize 2017
 Problems for Imre Bárány’s Birthday!
Top Posts & Pages
 Elchanan Mossel's Amazing Dice Paradox (your answers to TYI 30)
 Friendship and Sesame, Maryam and Marina, Israel and Iran
 TYI 30: Expected number of Dice throws
 Answer: Lord Kelvin, The Age of the Earth, and the Age of the Sun
 A Breakthrough by Maryna Viazovska Leading to the Long Awaited Solutions for the Densest Packing Problem in Dimensions 8 and 24
 The Race to Quantum Technologies and Quantum Computers (Useful Links)
 Touching Simplices and Polytopes: Perles' argument
 Test your intuition 29: Diameter of various random trees
 R(5,5) ≤ 48
RSS
Category Archives: Open problems
Touching Simplices and Polytopes: Perles’ argument
Joseph Zaks (1984), picture taken by Ludwig Danzer (OberWolfach photo collection) The story I am going to tell here was told in several places, but it might be new to some readers and I will mention my own angle, … Continue reading
Posted in Combinatorics, Convex polytopes, Geometry, Open problems
Tagged Joseph Zaks, Micha A. Perles
Leave a comment
R(5,5) ≤ 48
The Ramsey numbers R(s,t) The Ramsey number R(s, t) is defined to be the smallest n such that every graph of order n contains either a clique of s vertices or an independent set of t vertices. Understanding the values … Continue reading
Posted in Combinatorics, Open problems, Updates
Tagged Brendan D. McKay, Vigleik Angeltveit
Leave a comment
Test Your Intuition (27) about the AlonTarsi Conjecture
On the occasion of Polymath 12 devoted to the Rota basis conjecture let me remind you about the AlonTarsi conjecture and test your intuition concerning a strong form of the conjecture. The sign of a Latin square is the product … Continue reading
Posted in Combinatorics, Open problems, Test your intuition
Tagged AlonTarsi conjecture, Polymath12
Leave a comment
Polymath10 conclusion
The Polymath10 project on the ErdosRado DeltaSystem conjecture took place over this blog from November 2015 to May 2016. I aimed for an easygoing project that people could participate calmly aside from their main research efforts and the duration of … Continue reading
Posted in Combinatorics, Open problems, Polymath10
Tagged polymath10, sunflower conjecture
4 Comments
Polymath 10 post 6: The ErdosRado sunflower conjecture, and the Turan (4,3) problem: homological approaches.
In earlier posts I proposed a homological approach to the ErdosRado sunflower conjecture. I will describe again this approach in the second part of this post. Of course, discussion of other avenues for the study of the conjecture are welcome. The purpose … Continue reading
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 CrootLevPach 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.
21 Comments
Stefan Steinerberger: The Ulam Sequence
This post is authored by Stefan Steinerberger. The Ulam sequence is defined by starting with 1,2 and then repeatedly adding the smallest integer that is (1) larger than the last element and (2) can be written as the sum of two … Continue reading
Polymath 10 Post 3: How are we doing?
The main purpose of this post is to start a new research thread for Polymath 10 dealing with the ErdosRado Sunflower problem. (Here are links to post 2 and post 1.) Here is a very quick review of where we … Continue reading
Posted in Combinatorics, Mathematics over the Internet, Open problems, Polymath10
Tagged polymath10, sunflower conjecture
104 Comments
More Reasons for Small Influence
Readers of the bigleague ToC blogs have already heard about the breakthrough paper An averagecase depth hierarchy theorem for Boolean circuits by Benjamin Rossman, Rocco Servedio, and LiYang Tan. Here are blog reports on Computational complexity, on the Shtetl Optimized, and of Godel … Continue reading