Category Archives: Open problems

Eran Nevo: g-conjecture part 4, Generalizations and Special Cases

This is the fourth in a series of posts by Eran Nevo on the g-conjecture. Eran’s first post was devoted to the combinatorics of the g-conjecture and was followed by a further post by me on the origin of the g-conjecture. Eran’s second post was about … Continue reading

Posted in Combinatorics, Convex polytopes, Guest blogger, Open problems | Tagged , | 2 Comments

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

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Problems for Imre Bárány’s Birthday!

  On June 18-23 2017 we will celebrate in Budapest the 70th birthday of Imre Bárány. Here is the webpage of the conference. For the occasion I wrote a short paper with problems in discrete geometry, mainly around Helly’s and … Continue reading

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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

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Test Your Intuition (27) about the Alon-Tarsi Conjecture

On the occasion of Polymath 12 devoted to the Rota basis conjecture let me remind you about the Alon-Tarsi conjecture and test your intuition concerning a strong form of the conjecture. The sign of a Latin square is the product … Continue reading

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Polymath10 conclusion

The Polymath10 project on the Erdos-Rado Delta-System conjecture took place over this blog from November 2015 to May 2016. I aimed for an easy-going project that people could participate calmly aside from their main research efforts and  the duration of … Continue reading

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Polymath 10 post 6: The Erdos-Rado sunflower conjecture, and the Turan (4,3) problem: homological approaches.

In earlier posts I proposed a homological approach to the Erdos-Rado 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

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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

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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

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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 Erdos-Rado 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 , | 104 Comments