Natalie J. Durgin

Harvey Mudd College Mathematics 2009

Final Thesis: Final Report: The Abelian Sandple Model on Symmetric Graphs
Thesis Proposal: The Abelian Sandpile Model and the Symmetric Sandpile Subgroup
Thesis Advisor: Professor Francis Edward Su
Second Reader: Professor David Perkinson (Reed College)
Thesis Talks: HMC midyear talk, Fall 2008
PCUM conference, Spring 2009

Abelian Sandpile Model and Symmetric Sandpile Subgroups

The abelian sandpile model, or chip-firing game, is a cellular automaton model on finite directed graphs often used to describe the phenomenon of self-organized criticality. Here we define the notion of a symmetric sandpile configuration, and show that such configurations form a subgroup of the sandpile group. Using these constructions, we explore various properties of this symmetric sandpile subgroup.

sandpile symmetric