Title: Local Representations of Tropical Linear Series

Abstract: Dave Jensen and Sam Payne have defined a rank r tropical linear series on a metric graph to be a subset of a complete linear series satisfying global properties that are analogous to those for linear series on algebraic curves. In trying to discover more about these objects, I have defined a local representation of tropical linear series using 01-arrays. For valence-2 points of the metric graph, these local representations can be completely characterized and are in bijection with permutation matrices. These arrays show some promising features for understanding tropical linear series and there is reason to believe that for higher valence points, a notion of higher dimensional permutation 01-arrays can characterize local representations.