Schur-Positve Symmetric Functions from Products: Log-Majorization, Total-Positivity, and PSD Matrices

For a polynomial $F(t) = 1 + a_1 t + a_2 t^2 +\dots + a_d t^d$ with coefficients in a $\mathbb{Q}$-algebra $\mathcal{R}$, we consider Schur-positivity of the symmetric function $Ω_F(\mathbf{x}) = \prod_{i \geq 1} F(x_i)$. Using work of Lindström and Gessel--Viennot, we give sufficient conditions for