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Abelian Sandpile Model On Symmetric Graphs, Natalie Durgin

HMC Senior Theses

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.