Tropical methods in Hurwitz-Brill-Noether theory

Splitting type loci are the natural generalizations of Brill-Noether varieties for curves with a distinguished map to projective line. We give tropical proof theorem H. Larson, showing that splitting have expected dimension general elements Hurwitz space. Our uses an explicit description on certain family curves. further show these connected in codimension one, and describe algorithm computing their cardinality when they zero-dimensional. provide conjecture numerical class loci, which we confirm number cases.