Chip-Firing on Infinite k-ary Trees

Rajarshi Mandal, Tanya Khovanova

Abstract: We use an infinite k-ary tree with a self-loop at the root as our underlying graph. We consider a chip-firing process starting with N chips at the root. We describe the stable configurations. We calculate the number of fires for each vertex and the total number of fires. We study a sequence of the number of root fires for a given k as a function of N and study its properties. We do the same for the total number of fires.