초록: I will talk about some ongoing collaborative work with David Klompenhouwer and Paolo Rossi. Starting from the question “what is the relationship between the DR hierarchies and the analogous constructions made with admissible covers”, we realized that in fact in Hurwitz theory even three-pointed invariants can be encoded in a way to give the generating functions good structural properties similar to the DR case. Further, a large class of invariants can be reconstructed from WDVV and minimal initial condition. In this talk we focus on the compact type/one part case (one branch point corresponds to full ramification) where the structure is more transparent.