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.