Date of Award
5-2018
Document Type
Thesis
Degree Name
Master of Science (MS)
College/School
College of Science and Mathematics
Department/Program
Mathematical Sciences
Thesis Sponsor/Dissertation Chair/Project Chair
Deepak Bal
Committee Member
Aihua Li
Committee Member
Jonathan Cutler
Abstract
The Candy Game begins with a finite number of players sitting in a circle, each with an initial amount of candy. At each time step, each player passes half of their pile to the player on their left (with odd sized stacks receiving an extra piece of candy). The original question was whether every initial distribution of candy results in every player holding the same number of pieces after a finite number of turns. For arbitrary initial distributions, we prove asymptotically tight bounds on the final amount of candy. The diffusion chip firing game assigns integral chip amounts to each vertex of a graph. At each time step, a vertex sends a chip to each neighbor who has less chips than itself. We show that this game on the infinite path, with bounded chip labels remains bounded for all time.
Recommended Citation
DeGaetani, Joseph, "Candy Sharing and Chip Firing Games on Graphs" (2018). Theses, Dissertations and Culminating Projects. 127.
https://digitalcommons.montclair.edu/etd/127