# Generating weighted Hurwitz numbers

## TL;DR

This paper introduces a method to generate weighted Hurwitz numbers using multicurrent correlators linked to KP tau-functions, enabling the computation of various types of weighted Hurwitz numbers through formal series expansions.

## Contribution

It presents a novel approach connecting multicurrent correlators and KP tau-functions to generate and compute weighted Hurwitz numbers in a unified framework.

## Key findings

- Derived formal Taylor series for weighted Hurwitz numbers
- Computed simple, rational, and quantum weighted Hurwitz numbers
- Established a new link between correlators and Hurwitz number generation

## Abstract

Multicurrent correlators associated to KP $\tau$-functions of hypergeometric type are used as generating functions for weighted Hurwitz numbers. These are expressed as formal Taylor series and used to compute generic, simple, rational and quantum weighted single Hurwitz numbers.