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Category Archives: Open problems
Some Problems
Four posts ago I wrote about three recent breakthroughs in combinatorics and in the following post I would like to mention some problems that I posed over the years that are loosely related to these advances. Rank of incidence matrices … Continue reading
A Nice Example Related to the Frankl Conjecture
Updates: 1. Peter Frankl brought to my attention that the very same example appeared in a paper by Dynkin and Frankl “Extremal sets of subsets satisfying conditions induced by a graph“. 2. Sam Hopkins gave a lovely reference to Ravi … Continue reading
Amazing: Justin Gilmer gave a constant lower bound for the union-closed sets conjecture
Frankl’s conjecture (aka the union closed sets conjecture) asserts that if is a family of subsets of [n] (=: ) which is closed under union then there is an element such that Justin Gilmer just proved an amazing weaker form … Continue reading
Open problem session of HUJI-COMBSEM: Problem #5, Gil Kalai – the 3ᵈ problem
This post continues to describe problems presented at our open problems session back in November 2020. Here is the first post in the series. Today’s problem was presented by me, and it was an old 1989 conjecture of mine. A … Continue reading
Open problem session of HUJI-COMBSEM: Problem #1, Nati Linial – Turan type theorems for simplicial complexes.
On November, 2020 we had a very nice open problem session in our weekly combinatorics seminar at HUJI. So I thought to have a series of posts to describe you the problems presented there. This is the first post in … Continue reading
Péter Pál Pach and Richárd Palincza: a Glimpse Beyond the Horizon
Prologue Consider the following problems: P3: What is the maximum density of a set A in without a 3-term AP? (AP=arithmetic progression.) This is the celebrated Cap Set problem and we reported here in 2016 the breakthrough results by … Continue reading
Posted in Combinatorics, Geometry, Number theory, Open problems
Tagged Péter Pál Pach, Richárd Palincza
9 Comments
Kelman, Kindler, Lifshitz, Minzer, and Safra: Towards the Entropy-Influence Conjecture
Let me briefly report on a remarkable new paper by Esty Kelman, Guy Kindler, Noam Lifshitz, Dor Minzer, and Muli Safra, Revisiting Bourgain-Kalai and Fourier Entropies. The paper describes substantial progress towards the Entropy-Influence conjecture, posed by Ehud Friedgut and … Continue reading
Posted in Combinatorics, Computer Science and Optimization, Open problems
Tagged Dor Minzer, Esty Kelman, Guy Kindler, Muli Safra, Noam Lifshitz
2 Comments
Ringel Conjecture, Solved! Congratulations to Richard Montgomery, Alexey Pokrovskiy, and Benny Sudakov
Ringel’s conjecture solved (for sufficiently large n) A couple weeks ago and a few days after I heard an excellent lecture about it by Alexey Pokrovskiy in Oberwolfach, the paper A proof of Ringel’s Conjecture by Richard Montgomery, Alexey Pokrovskiy, … Continue reading
Posted in Combinatorics, Open problems, Updates
Tagged Alexey Pokrovskiy, Benny Sudakov, Richard Montgomery
5 Comments
Test your intuition 43: Distribution According to Areas in Top Departments.
In the community of mamathetitians in a certain country there are mamathetitians in two areas: Anabra (fraction p of the mamathetitians) and Algasis (fraction 1-p of mamathetitians.) There are ten universities with 50 faculty members in each mamathetics department … Continue reading
Posted in Combinatorics, Open problems, Probability, Test your intuition
Tagged Test your intuition
9 Comments
Gérard Cornuéjols’s baker’s eighteen 5000 dollars conjectures
Gérard Cornuéjols Gérard Cornuéjols‘s beautiful (and freely available) book from 2000 Optimization: Packing and Covering is about an important area of combinatorics which is lovely described in the preface to the book The integer programming models known as set packing … Continue reading
Combinatorics and more 