Applications of stable polynomials to mixed determinants: Johnson's conjectures, unimodality, and symmetrized Fischer products

Julius Borcea, Petter Brändén

For $n\times n$ matrices $A$ and $B$ define $$\eta (A,B)=\sum _S\det (A[S])\det (B[S^{\prime }]),$$ where the summation is over all subsets of $\{1,...,n\}$, $S^{\prime }$ is the complement of $S$, and…