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Category Archives: Combinatorics
Mathematics (mainly combinatorics) related matters: A lot of activity.
Plan for next weeks blogging There are various things to blog about and let me give a quick preview for the plan for the next few posts. The purpose of this post is to give an impression about the hectic … Continue reading
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
An Aperiodic Monotile
I suppose that most of you have already heard about the first ever aperiodic planar tiling with one type of tiles. It was discovered by David Smith, Joseph Samuel Myers, Craig S. Kaplan, and Chaim Goodman-Strauss. Amazing!!! Update (May … Continue reading
Posted in Combinatorics, Geometry, Updates
Tagged Chaim Goodman-Strauss, Craig S. Kaplan, David Smith, Joseph Samuel Myers
12 Comments
Some News from a Seminar in Cambridge
On an old problems of Erdős (h/t Michael Simkin and Nati Linial) Here is a somewhat mysterious announcement for a combinatorics seminar lecture at Cambridge. Which old problems of Erdős are we talking about? Here is a picture from the … Continue reading
Posted in Combinatorics, Test your intuition
Tagged Julian Sahasrabudhe, Marcelo Campos, Paul Erdos, Rob Morris, Simon Griffiths
12 Comments
Subspace Designs, Unit and Distinct Distances, and Piercing Standard Boxes.
A lot of things are happening and let me briefly report on three major advancements in combinatorics. Peter Keevash, Ashwin Sah and Mehtaab Sawhney proved the existence of subspace designs with any given parameters, provided that the dimension of the … Continue reading
Posted in Combinatorics, Geometry
Tagged Ashwin Sah, István Tomon, Lisa Sauermann, Matija Bucić, Mehtaab Sawhney, Noga Alon, Peter Keevash
4 Comments
Greg Kuperberg @ Tel Aviv University
Greg Kuperberg is on a short visit in Israel and yesterday he gave a fantastic lecture on an improved bound for the Solovay-Kitaev theorem. Here is a videotaped lecture of Greg on the same topic in QIP2023. The Solovay-Kitaev theorem … Continue reading
Posted in Algebra, Combinatorics, Computer Science and Optimization, Quantum
Tagged Greg Kuperberg
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Absolutely Sensational Morning News – Zander Kelley and Raghu Meka proved Behrend-type bounds for 3APs
What is the density of a subset of that guarantees that contains a 3-term arithmetic progression? And, more generally, if the density of is what is the minimum number of 3-terms AP that contains? These problems and the more general … 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
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