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.
