Monthly Archives: January 2024

On the Limit of the Linear Programming Bound for Codes and Packing

Posted on January 21, 2024 by Gil Kalai

Alex Samorodnitsky The most powerful general method for proving upper bounds for the size of error correcting codes and of spherical codes (and sphere packing) is the linear programming method that goes back to Philippe Delsarte. There are very interesting … Continue reading →

Posted in Combinatorics, Convexity, Geometry | Tagged , , , | 3 Comments

TYI 54: A Variant of Elchanan Mossel’s Amazing Dice Paradox

Posted on January 16, 2024 by Gil Kalai

The following question was inspired by recent comments to the post on Elchanan Mossel’s amazing Dice Paradox. A fair dice is a dice that when thrown you get each of the six possibilities with probability 1/6. A random dice is … Continue reading →

Posted in Probability, Test your intuition | Tagged , | 14 Comments

Riddles (Stumpers), Psychology, and AI.

Posted on January 2, 2024 by Gil Kalai

Two months ago I presented five riddles and here, in this post, you will find a few more. (These types of riddles are called by Maya Bar-Hillel “stumpers”.) This time, we will have a discussion about how riddles are related … Continue reading →

Posted in AI, Computer Science and Optimization, Philosophy, Psychology | Tagged , , , | 10 Comments

Soma Villanyi: Every d(d+1)-connected graph is globally rigid in d dimensions.

Posted on January 1, 2024 by Gil Kalai

Today, I want to tell you a little about the following paper that solves a conjecture of Laszlo Lovász and Yechiam Yemini from 1982 and an even stronger conjecture of Bob Connelly, Tibor Jordán, and Walter Whiteley from 2013: Every … Continue reading →

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