## The Cube Recurrence and Groves

## Oliver Cheng (Brown)

#### Abstract :

The cube recurrence is an equation with the vertices of a cube as
variables. We use it to determine the eighth vertex weight from the other
seven, which corresponds nicely to adding or removing a cube from a stack
of cubes. I will introduce all these things, and then discuss their
relation to certain graphs on those cubes called groves. We then use this
relation to count groves and explore their shape.