7 problems

For $g\geq 0$, $n\geq 1$, and $(g,n)\neq(0,1),(0,2)$, let $H^g_{(d),\beta}$ be the one-part double Hurwitz number, let $r^g_{(d),\beta}$ be its associated number of simple branch p…

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…

Top-term conjecture. The top term of $H_g(\mu^{(1)},\dots,\mu^{(s)};T)$ is

Let $h_{g;\mu_1,\ldots,\mu_n}^{\textnormal{one-part}}$ denote the double Hurwitz number with one ramification profile equal to the one-part partition of size…

Let $DH_{g,n}(\mu_1,\ldots,\mu_n)$ be the double Hurwitz numbers, and let $d$ and $A_\mu^i$ be defined by … where $\lambda$ is an integer partition with $\ell(\lambda)$ parts and…

Let $F_{g,n}$ be the free-energy generating functions associated with the double Hurwitz numbers, let $a_1,\ldots,a_d$ be the branch points of the spectral curve, and let…

Let $d$ be a positive integer, let $q_1,\ldots,q_d$ be parameters, and set … Consider the rational spectral curve … Let $DH_{g,n}(\mu_1,\ldots,\mu_n)$ denote the associated double…