  We show that tropicalization of linear series on curves gives rise to
two-parameter families of tilings by polymatroids, with one parameter arising
from the theory of divisors on tropical curves and the other from the reduction
of linear series of rational functions in non-Archimedean geometry. In order to
do this, we introduce a general framework that produces tilings of vector
spaces and their subsets by polymatroids. We furthermore show that these
tilings are regular and relate them to work by Kapranov and Lafforgue on Chow
quotients of Grassmannians.
