Immanant Inequalities and Partition Node Diagrams
Thomas H. Pate · Journal of the London Mathematical Society · 1992
If α is a partition of n then d ¯ α denotes the associated normalized immanant. It is shown that if α = {α1,…,α8,…,αt} is a non-increasing partition of n with α8 > max {α8+1, 1} and α′ denotes the partition {α1,…,α8−1,…,α8+1,…αt, 1} then d ¯ α(A) ⩾ d ¯ α′(A) for each n×n positive semi-definite Hermitian matrix A.