The positivity conjecture for normalized Macdonald structure coefficients

Let $\boldsymbol{g}^\pi_{\mu,\nu}(\alpha,\gamma)$ be the Macdonald structure coefficients introduced in the paper, let $b:=\alpha-1$, and define

$$f(n_1,n_2,k):=(M-m)(M+m-k)+m(m-1)-(k-M)(k-M-1),$$

where $M=\max(n_1,n_2)$ and $m=\min(n_1,n_2)$. For partitions $\pi,\mu,\nu$, use the coefficients $\boldsymbol{g}^\pi_{\mu,\nu}$ and the partition-size parameters in this function.

The positivity conjecture. Let $\pi,\mu,\nu$ be three partitions. Then

$$(1+\gamma)^{f(|\mu|,|\nu|,|\pi|)}z_\mu z_\nu\boldsymbol{g}^\pi_{\mu,\nu}$$

is a polynomial in $b:=\alpha-1$ and $\gamma$ with non-negative integer coefficients. The supplied text gives no resolution evidence for this conjecture.