An inequality for subpermanents of positive semidefinite hermitian matrices

Abstract

Let A an n×n p.s.d hermitian matrix, let r ₁…r _n denote the row sums of A, and suppose . Denote by p_k (A) the sum of permanents of all kxk submatrices of A. It is shown that of 2≤k≤n the

It follows that of J_R denotes the n×n matrix whose (i,j) entry is then the function P_k ((1−t)J_R +tA) is non-decreasing on [0,1].