PRIMER FOR THE ALGEBRAIC GEOMETRY OF SANDPILES

@article{Perkinson2009PRIMERFT,
  title={PRIMER FOR THE ALGEBRAIC GEOMETRY OF SANDPILES},
  author={David Perkinson and Jacob Perlman and John Wilmes},
  journal={arXiv: Combinatorics},
  year={2009}
}
The Abelian Sandpile Model (ASM) is a game played on a graph realizing the dynamics implicit in the discrete Laplacian matrix of the graph. The purpose of this primer is to apply the theory of lattice ideals from al- gebraic geometry to the Laplacian matrix, drawing out connections with the ASM. A extended summary of the ASM and of the required algebraic ge- ometry is provided. New results include a characterization of graphs whose Laplacian lattice ideals are complete intersection ideals; a… 
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