# Computing Linear Systems on Metric Graphs

### Abstract

The linear system of a divisor $D$ on a metric graph has the structure of a cell complex. We introduce the anchor divisors and anchor cells in it – they serve as the landmarks for us to compute the $f$-vector of the complex and find all cells in the complex. A linear system can also be identified as a tropical convex hull of rational functions. We compute its extremal generators using the landmarks. We apply these methods to some examples – namely the canonical linear systems of some small trivalent graphs.

Type
Publication
Journal of Symbolic Computation, 2018, 87(3), 54-67
##### Bo Lin
###### Visiting Assistant Professor

My research interests include mathematical biology, tropical geometry and combinatorics.