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


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.

How to Cite
Borodin, M., Han, H., Ji, K., Khovanova, T., Peng, A., Sun, D., Tu, I., Yang, J., Yang, W., Zhang, K., & Zhao, K. (2021). Chip-Firing and Fractional Bases. Minnesota Journal of Undergraduate Mathematics, 6(1). Retrieved from