Fomin–Fulton–Li–Poon conjecture for skew partitions

Let $\mu/\alpha$ and $\nu/\beta$ be skew partitions, with skew Schur functions $s_{\mu/\alpha}$ and $s_{\nu/\beta}$. Extend the star operation to pairs of skew partitions by

$${(\mu/\alpha,\nu/\beta)}^*:={(\mu,\nu)}^*/{(\alpha,\beta)}^*.$$

Write $(\lambda,\rho)={(\mu/\alpha,\nu/\beta)}^*$, and call a symmetric function Schur-positive when all coefficients in its Schur-function expansion are non-negative integers.

Fomin–Fulton–Li–Poon conjecture for skew partitions. For any skew partitions $\mu/\alpha$ and $\nu/\beta$, if

$$(\lambda,\rho)={(\mu/\alpha,\nu/\beta)}^*,$$

then the symmetric function

$$s_{\lambda}s_{\rho}-s_{\mu/\alpha} s_{\nu/\beta}$$

is Schur-positive.

This is presented as an extension of the preceding Fomin–Fulton–Li–Poon conjecture, motivated by computer experiments and the preservation of several families of pairs of skew shapes under the extended star operation. Its status is not resolved in the supplied source context.