Supersymmetric Latin Squares « Cap’s Whiteboard

3 July 2011

Back after a long hiatus on Cap’s Whiteboard, today I talk a little about a combinatorics problem I’ve been playing with.  I’m hoping to classify  Latin squares which satsify a strong symmetry condition.

Permalink: Supersymmetric Latin Squares « Cap’s Whiteboard.

CW: Cutting a rectangle into smaller rectangles

3 August 2010

This time on Cap’s Whiteboard, a quickie gem about combinatorial geometry. Is it possible to start with a rectangle, neither of whose sides has integral length, and cut it into smaller rectangular pieces, each of which has at least one integral side?

It has been said (by the mathematician Alain Connes) that you cannot understand the integers unless you understand this.

Permalink: Rectangles with an Integral Side Length

CW: The integers are a topological space?

10 July 2010

This time on Cap’s Whiteboard, some remarks on an undeservedly-little-known proof that there are infinitely many prime numbers, which works by treating \mathbb{Z} as a topological space, a bit of ingenuity due to Furstenburg (as far as I know).

Permalink: Idle remarks on the Furstenburg topology

CW: Counting Problems in Apollonian Circle Packings

8 July 2010

The first “real” post on Cap’s Whiteboard. I talk a little about the counting problem that kicked off my study of Apollonian circle packings.

It all starts with this picture.

Apollonian circle packing with root quadruple (-1,2,2,3)Apollonian circle packing with root quadruple (-1,2,2,3)

Permalink: Counting Problems in Apollonian Circle Packings