SIGNED CHIP FIRING GAMES AND SYMMETRIC SANDPILE MODELS ON THE CYCLES
We investigate the Sandpile Model and Chip Firing Game and an extension of these models on cycle graphs. The extended model consists of allowing a negative number of chips at each vertex. We give the characterization of reachable configurations and of fixed points of each model. At the end, we give explicit formula for the number of their fixed points.
signed chip firing game chip firing game symmetric sandpile model sandpile model circular distribution lattice structure