Behrend’s Construction

How large can a set of integers be without containing any 3-term arithmetic progressions? German mathematician Felix Behrend provided a construction in 1946 which gave an example of a fairly large set lacking such progressions. The main idea of the work is to use the fact that a line may intersect with a sphere . . . [Read More]

A Dinner Party Problem

Figure 1This is a classic introductory result in combinatorics. Suppose that six people are gathered at a dinner party. Then there is a group of three people at the party who are either all mutual acquaintances or all mutual strangers.

To formalize . . . [Read More]