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The Identity of the Abelian Sandpile Group

Doman, Noah (2020) The Identity of the Abelian Sandpile Group. Bachelor's Thesis, Mathematics.


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Sandpiles, or configurations, are non-negative integer vectors indexed by the vertices of a finite connected graph. Under toppling, the set of stable configurations forms a finite commutative monoid. One possible definition of the abelian sandpile group is that it is the minimal ideal of this monoid. The identity element of the group is a particular configuration; in the case of a graph with symmetries (for example, a square grid), it possesses a fractal-like structure. In this bachelor's project, our main focus is on the abelian sandpile group of undirected rectangular grid graphs, and we present two different methods for calculating its identity. We also discuss the symmetric aspects of the identity element, and the existence of the symmetric abelian sandpile subgroup.

Item Type: Thesis (Bachelor's Thesis)
Supervisor name: Top, J.
Degree programme: Mathematics
Thesis type: Bachelor's Thesis
Language: English
Date Deposited: 14 Jan 2020 10:10
Last Modified: 14 Jan 2020 10:10

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