Enumerating linear systems on graphs

@article{Brauner2020EnumeratingLS,
  title={Enumerating linear systems on graphs},
  author={Sarah Brauner and Forrest Glebe and David Perkinson},
  journal={Mathematische Zeitschrift},
  year={2020}
}
The divisor theory of graphs views a finite connected graph $G$ as a discrete version of a Riemann surface. Divisors on $G$ are formal integral combinations of the vertices of $G$, and linear equivalence of divisors is determined by the discrete Laplacian operator for $G$. As in the case of Riemann surfaces, we are interested in the complete linear system $|D|$ of a divisor $D$---the collection of nonnegative divisors linearly equivalent to $D$. Unlike the case of Riemann surfaces, the complete… 
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Simplicial Dollar Game
The dollar game is a chip-firing game introduced by Baker as a context in which to formulate and prove the Riemann-Roch theorem for graphs. A divisor on a graph is a formal integer sum of vertices.
Necklaces and slimes

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