IMMANANT INEQUALITIES AND PARTITION NODE DIAGRAMS

If alpha is a partition of n then d(alpha)BAR denotes the associated normalized immanant. Its shown that if alpha = {alpha1,...,alpha(s),...,alpha(t)} is a non-increasing partition of n with alpha(s) > max {alpha(s+1), 1} and alpha' denotes the partition {alpha1,...,alpha(s)-1,alpha(s+1),...,alpha(t),1} then d(alpha)(A)BAR greater-than-or-equal-to d(alpha')(A)BAR for each n x n positive semi-definite Hermitian matrix A.