Monthly Archives: March 2018

A Wonderful Paper by Igor Pak: Complexity Problems in Enumerative Combinatorics

Posted on March 31, 2018 by Gil Kalai

Greetings from Sa Pa in the very north of Vietnam. Let me recommend a  great thought-provoking paper by Igor Pak:  Complexity problems in enumerative combinatorics. As Igor wrote on his blog: Well, I finally finished my ICM paper. It’s only 30 … Continue reading →

Posted in Combinatorics | Tagged , | Leave a comment

Frankl’s Conjecture for Large Families: Ilan Karpas’ Proof

Posted on March 9, 2018 by Gil Kalai

Frankl’s conjecture asserts that a for every finite family of of finite sets that is closed under union, there is an element that belongs to at least half the sets in the family. We mentioned the problem in our very … Continue reading →

Posted in Combinatorics, Mathematics over the Internet, Open problems | Tagged , , , | 12 Comments

Test your intuition 33: Why is the density of any packing of unit balls decay exponentially with the dimension?

Posted on March 5, 2018 by Gil Kalai

Test your intuition: What is the simplest explanation you can give to the fact that the density of every packing of unit balls in is exponentially small in ? Answers are most welcome. Of course, understanding the asymptotic behavior of … Continue reading →

Posted in Combinatorics, Geometry, Test your intuition | Tagged , | 4 Comments