# Wall-crossing and recursion formulae for tropical Jucys covers

## TL;DR

This paper uses tropical geometry techniques to prove piecewise polynomiality and derive new wall-crossing formulas for monotone double Hurwitz numbers, advancing understanding of their enumerative properties.

## Contribution

It introduces a novel application of tropical flows to establish polynomiality and wall-crossing formulas for monotone double Hurwitz numbers.

## Key findings

- Proof of piecewise polynomiality of monotone double Hurwitz numbers
- Derivation of new wall-crossing formulas
- Enhanced understanding of tropical interpretations in enumerative geometry

## Abstract

In recent work, the authors derived a tropical interpretation of monotone and strictly monotone double Hurwitz numbers. In this paper, we apply the technique of tropical flows to this interpretation in order to provide a new proof of the piecewise polynomiality of these enumerative invariants. Moreover, we derive new types of wall-crossing formulae.