Graduation Year
2009
Document Type
Open Access Senior Thesis
Degree Name
Bachelor of Science
Department
Mathematics
Reader 1
Francis Su
Reader 2
David Perkinson (Reed College)
Abstract
The abelian sandpile model, or chip firing game, is a cellular automaton on finite directed graphs often used to describe the phenomenon of self organized criticality. Here we present a thorough introduction to the theory of sandpiles. Additionally, we define a symmetric sandpile configuration, and show that such configurations form a subgroup of the sandpile group. Given a graph, we explore the existence of a quotient graph whose sandpile group is isomorphic to the symmetric subgroup of the original graph. These explorations are motivated by possible applications to counting the domino tilings of a 2n × 2n grid.
Recommended Citation
Durgin, Natalie, "Abelian Sandpile Model on Symmetric Graphs" (2009). HMC Senior Theses. 217.
https://scholarship.claremont.edu/hmc_theses/217
