Chip-Firing and Fractional Bases

Matvey Borodin

Michael Driscoll School

Hannah Han

Kaylee Ji

Tanya Khovanova

Alexander Peng

David Sun

Isabel Tu

Jason Yang

William Yang

Kevin Zhang

Kevin Zhao


Abstract

We study a particular chip-firing process on the one-dimensional lattice. At any time when there are at least a+b chips at a vertex, a chips fire to the left and b chips fire to the right. We describe the final state of this process when we start with n chips at the origin.