Sniady's positivity conjecture for hypermap coefficients

Let $\pi$, $\mu$, and $\nu$ be partitions, and let $g^\pi_{\mu,\nu}$ denote the corresponding hypermap coefficient. Set $b:=\alpha-1$. Sniady's conjecture. For any partitions $\pi$, $\mu$, and $\nu$, $g^\pi_{\mu,\nu}$ is a polynomial in $b$ with non-negative integer coefficients. This conjecture generalizes the Matching-Jack conjecture to coefficients indexed by partitions of arbitrary sizes and remains open.