Enumerating linear systems on graphs

  title={Enumerating linear systems on graphs},
  author={Sarah Brauner and Forrest Glebe and David Perkinson},
  journal={Mathematische Zeitschrift},
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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