Conditional subadditivity for submodular functions yields strengthened Szász's and Fischer's inequalities that are strictly tighter than the classical statements for non-diagonal positive definite matrices.
Nonnegative entropy measures of multivariate symmetric correlations
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From Submodularity to Matrix Determinants: Strengthening Han's, Sz\'asz's, and Fischer's Inequalities
Conditional subadditivity for submodular functions yields strengthened Szász's and Fischer's inequalities that are strictly tighter than the classical statements for non-diagonal positive definite matrices.