Category Archives: Combinatorics

Alef Corner: ICM2022

Alef’s new piece for ICM 2022 will surely cheer you up!

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To cheer you up in difficult times 22: some mathematical news! (Part 1)

To cheer you up, in these difficult times, here are (in two parts) some mathematical news that I heard in personal communications or on social media. (Maybe I will write later, in more details,  about few of them that are … Continue reading

Posted in Combinatorics, Convex polytopes, Convexity, Geometry | Leave a comment

Cheerful News in Difficult Times: The Abel Prize is Awarded to László Lovász and Avi Wigderson

The Abel Prize was awarded earlier today to László Lovász and Avi Wigderson “for their foundational contributions to theoretical computer science and discrete mathematics, and their leading role in shaping them into central fields of modern mathematics.” Congratulations to Laci … Continue reading

Posted in Combinatorics, Computer Science and Optimization, Convexity, Geometry, Updates | Tagged , , , | 3 Comments

Nostalgia corner: John Riordan’s referee report of my first paper

In 1971/1972 academic year, I was an undergraduate student at the Hebrew University of Jerusalem and toward the end of the year I wrote a paper about Abel’s sums. I sent it to John Riordan the author of the books  … Continue reading

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To cheer you up in difficult times 20: Ben Green presents super-polynomial lower bounds for off-diagonal van der Waerden numbers W(3,k)

What will be the next polymath project? click here for our post about it.  New lower bounds for van der Waerden numbers by Ben Green Abstract: We show that there is a red-blue colouring of [N] with no blue 3-term … Continue reading

Posted in Combinatorics, Number theory | Tagged , | 2 Comments

To cheer you up in difficult times 19: Nati Linial and Adi Shraibman construct larger corner-free sets from better numbers-on-the-forehead protocols

What will be the next polymath project? click here for our previous post.  Number on the forehead, communication complexity, and additive combinatorics Larger Corner-Free Sets from Better NOF Exactly-N Protocols, by Nati Linial and Adi Shraibman Abstract: A subset of … Continue reading

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Possible future Polymath projects (2009, 2021)

What will be our next polymath project? A polymath project (Wikipedia) is a collaboration among mathematicians to solve important and difficult mathematical problems by coordinating many mathematicians to communicate with each other on finding the best route to the solution. … Continue reading

Posted in Combinatorics, Mathematics over the Internet, Open discussion | Tagged , , | 23 Comments

Amazing: Simpler and more general proofs for the g-theorem by Stavros Argyrios Papadakis and Vasiliki Petrotou, and by Karim Adiprasito, Stavros Argyrios Papadakis, and Vasiliki Petrotou.

Stavros Argyrios Papadakis, Vasiliki Petrotou, and Karim Adiprasito In 2018, I reported here about Karim Adiprasito’s proof of the g-conjecture for simplicial spheres.  This conjecture by McMullen from 1970 was considered a holy grail of algebraic combinatorics and it resisted … Continue reading

Posted in Algebra, Combinatorics, Geometry | Tagged , , , , | 5 Comments

Igor Pak: What if they are all wrong?

Originally posted on Igor Pak's blog:
Conjectures are a staple of mathematics. They are everywhere, permeating every area, subarea and subsubarea. They are diverse enough to avoid a single general adjective. They come in al shapes and sizes. Some…

Posted in Combinatorics, Computer Science and Optimization, Geometry, What is Mathematics | Tagged | 6 Comments

To cheer you up in difficult times 17: Amazing! The Erdős-Faber-Lovász conjecture (for large n) was proved by Dong Yeap Kang, Tom Kelly, Daniela Kühn, Abhishek Methuku, and Deryk Osthus!

Dong Yeap Kang, Tom Kelly, Daniela Kühn, Abhishek Methuku, and Deryk Osthus have just uploaded a paper to the arXive, A proof of the Erdős-Faber-Lovász conjecture. (I am thankful to Nati Linial and Ryan Alweiss for telling me about it.) … Continue reading

Posted in Combinatorics, Updates | Tagged , , , , , | 4 Comments