2 problems

Fix $g$, $m$, and $n$, and let $P^{g}_{m,n}(\alpha_1,\dots,\alpha_m,\beta_1,\dots,\beta_n)=H^{g}_{\alpha,\beta}$ on the tuples of positive integers satisfying…

Let $\mathbf{x}=(x_1,\ldots,x_n)\in\mathbb Z^n$ satisfy $\sum_i x_i=0$, and let $H_g^r(\mathbf{x})$ be the double Hurwitz number, viewed piecewise polynomially on the chambers of t…