Exploring the Algebraic Properties of Sandpile Models

Student: Nazirbekova Aizhana

Educational Programme: Mathematics (Bachelor)

Year of Graduation: 2021

A sandpile is a collection of indistinguishable particles (sand grains, chips) on the graph. All stable configurations on this model organize a commutative monoid. And the minimal ideal of this monoid is a abelian sandpile group. The neutral element in this group is a certain configuration, which has a fractal structure when it comes to symmetric graphs. In this project my main goal is to show you the abelian sandpile group of finite symmetric graphs, describe its algebraic properties, demonstrate method for finding a neutral element and calculate it on some graphs of various sizes.

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