Monthly Archives: July 2019

TYI 39 : Can a coalition of children guarantees all being in the same class?

There is a class of children that have just finished elementary school. Now they all move from elementary school to high school and classes are reshuffled. Each child lists three friends, and the assignment of children into classes ensures that … Continue reading

Posted in Combinatorics, Economics, Mathematics to the rescue, Test your intuition | Tagged | Leave a comment

Matan Harel, Frank Mousset, and Wojciech Samotij and the “the infamous upper tail” problem

Let me report today on a major breakthrough in random graph theory and probabilistic combinatorics. Congratulations to Matan, Frank, and Vojtek! Artist: Heidi Buck. “Catch a Dragon by the Tail 2” ( source ) Upper tails via high moments and entropic … Continue reading

Posted in Combinatorics, Probability | Tagged , , | 1 Comment

Isabella Novik and Hailun Zheng: Neighborly centrally symmetric spheres exist in all dimensions!

A tweet-long summary: The cyclic polytope is wonderful and whenever we construct an analogous object we are happy. Examples: Neighborly cubic polytopes; The amplituhedron; and as of last week, the Novik-Zheng new construction of neighborly centrally symmetric spheres! At last: … Continue reading

Posted in Combinatorics, Convexity | Tagged , | Leave a comment

Dan Romik on the Riemann zeta function

This post, about the Riemann zeta function, which is among the most important and mysterious mathematical objects was kindly written by Dan Romik. It is related to his paper Orthogonal polynomial expansions for the Riemann xi function,  that we mentioned … Continue reading

Posted in Combinatorics, Guest blogger, Number theory | Tagged , , , , | 1 Comment

Itai Benjamini and Jeremie Brieussel: Noise Sensitivity Meets Group Theory

The final  version of my ICM 2018 paper Three puzzles on mathematics computation and games has been available for some time. (This proceedings’ version, unlike the arXived version has a full list of references.)  In this post I would like to … Continue reading

Posted in Algebra, Combinatorics, Probability | Tagged , , | 1 Comment

Imre Bárány: Limit shape

Limit shapes are fascinating objects in the interface between probability and geometry and between the discrete and the continuous. This post is kindly contributed by Imre Bárány. What is a limit shape? There are finitely many convex lattice polygons contained … Continue reading

Posted in Combinatorics, Convexity, Geometry, Guest blogger, Probability | Tagged , | 4 Comments

Amazing: Hao Huang Proved the Sensitivity Conjecture!

Today’s arXived amazing paper by Hao Huang Induced subgraphs of hypercubes and a proof of the Sensitivity Conjecture Contains an amazingly short and beautiful proof of a famous open problem from the theory of computing – the sensitivity conjecture posed … Continue reading

Posted in Combinatorics, Computer Science and Optimization | Tagged , | 18 Comments