Category Archives: Combinatorics

A Nice Example Related to the Frankl Conjecture

Update: 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“. The example As a follow up to my previous post … Continue reading

Posted in Combinatorics, Open discussion, Open problems | Tagged , , , , , , , , , , | 7 Comments

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

Posted in Combinatorics, Open problems | Tagged , , | 17 Comments

James Davies: Every finite colouring of the plane contains a monochromatic pair of points at an odd distance from each other.

Here is a lovely piece of news: the following paper by James Davies was posted on the arXive a few weeks ago. The paper uses spectral methods to settle an old question, posed in 1994, by Moshe Rosenfeld. (See this … Continue reading

Posted in Combinatorics, Geometry | Tagged , | 1 Comment

Alexander A. Gaifullin: Many 27-vertex Triangulations of Manifolds Like the Octonionic Projective Plane (Not Even One Was Known Before).

  From top left clockwise: Alexander Gaifullin, Denis Gorodkov, Ulrich Brehm, Wolfgang Kühnel  Here is the paper: Alexander A. Gaifullin: 634 vertex-transitive and more than 10¹⁰³ non-vertex-transitive 27-vertex triangulations of manifolds like the octonionic projective plane  Abstract with annotation: In … Continue reading

Posted in Combinatorics, Geometry | Tagged , , , | 2 Comments

ICM 2022 awarding ceremonies (1)

Hugo Duminil-Copin, June Huh, James Maynard and Maryna Viazovska were awarded the Fields Medal 2022 and Mark Braverman was awarded the Abacus Medal 2022. I am writing from Helsinki where I attended the meeting of the General Assembly of the … Continue reading

Posted in Academics, Algebra, Applied mathematics, Combinatorics, Computer Science and Optimization, Convexity, Geometry, ICM2022, Probability | 7 Comments

Richard Stanley: Enumerative and Algebraic Combinatorics in the1960’s and 1970’s

In his comment to the previous post by Igor Pak, Joe Malkevitch referred us to a wonderful paper by Richard Stanley on enumerative and algebraic combinatorics in the 1960’s and 1970’s. See also this post on Richard’s memories regarding the … Continue reading

Posted in Combinatorics, What is Mathematics | Tagged | 1 Comment

Igor Pak: How I chose Enumerative Combinatorics

Originally posted on Igor Pak's blog:
Apologies for not writing anything for awhile. After Feb 24, the math part of the “life and math” slogan lost a bit of relevance, while the actual events were stupefying to the point…

Posted in Combinatorics, What is Mathematics | Tagged | 1 Comment

Oliver Janzer and Benny Sudakov Settled the Erdős-Sauer Problem

Norbert Sauer The news in brief:  In the new paper Resolution of the Erdős-Sauer problem on regular subgraphs Oliver Janzer and Benny Sudakov proved that any graph G with vertices and more than edges contains a k-regular subgraph. This bound … Continue reading

Posted in Combinatorics | Tagged , | 7 Comments

Past and Future Events

Quick announcements of past (recorded) and future events 1) Shachar Lovett was the Erdos Speaker for 2022 and his great talks are recorded. (Lecture 1, Tensor ranks and their applications lecture 2, The monomial structure of Boolean functions, lecture 3, … Continue reading

Posted in Combinatorics, Conferences, Convexity, Geometry, Quantum | Leave a comment

Joshua Hinman proved Bárány’s conjecture on face numbers of polytopes, and Lei Xue proved a lower bound conjecture by Grünbaum.

Joshua Hinman proved Bárány’s conjecture. One of my first posts on this blog was a 2008 post Five Open Problems Regarding Convex Polytopes, now 14 years later, I can tell you about the first problem on the list to get solved. … Continue reading

Posted in Combinatorics, Convex polytopes | Tagged , , , | 5 Comments