Spencer Backman, The generalized cycle-cocycle reversal system for partial graph orientations

We introduce a discrete dynamical system on the set of partial orientations of a graph, which generalizes Gioan’s cycle-cocycle reversal system. We explain how this setup allows for a new interpretation of the linear equivalence of divisors on graphs (chip-firing), and a new proof of Baker and Norine’s combinatorial Riemann-Roch formula. Fundamental connections to the max-flow min-cut theorem will be highlighted.