# 2D Toda τ functions, weighted Hurwitz numbers and the Cayley graph: Determinant representation and recursion formula

@article{Ding20222DT, title={2D Toda $\tau$ functions, weighted Hurwitz numbers and the Cayley graph: Determinant representation and recursion formula}, author={Xiang-Mao Ding and Xiang Li}, journal={Journal of Mathematical Physics}, year={2022} }

We generalize the determinant representation of the Kadomtsev–Petviashvili τ functions to the case of the 2D Toda τ functions. The generating functions for the weighted Hurwitz numbers are a parametric family of 2D Toda τ functions, for which we give a determinant representation of weighted Hurwitz numbers. Then, we can get a finite-dimensional equation system for the weighted Hurwitz numbers [Formula: see text] with the same dimension | σ| = | ω| = n. Using this equation system, we calculated…

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