# Riemann-Roch Theory for Graph Orientations

@article{Backman2014RiemannRochTF,
title={Riemann-Roch Theory for Graph Orientations},
author={Spencer Backman},
journal={ArXiv},
year={2014},
volume={abs/1401.3309}
}
We develop a new framework for investigating linear equivalence of divisors on graphs using a generalization of Gioan's cycle--cocycle reversal system for partial orientations. An oriented version of Dhar's burning algorithm is introduced and employed in the study of acyclicity for partial orientations. We then show that the Baker--Norine rank of a partially orientable divisor is one less than the minimum number of directed paths which need to be reversed in the generalized cycle--cocycle… Expand
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