Immanant Inequalities and Partition Node Diagrams

If α is a partition of n then d ¯ α denotes the associated normalized immanant. It is shown that if α = {α 1 ,…,α 8 ,…,α t } is a non‐increasing partition of n with α 8 > max {α 8+1 , 1} and α′ denotes the partition {α 1 ,…,α 8 −1,…,α 8+1 ,…α t , 1} then d ¯ α ( A ) ⩾ d ¯ α′ ( A ) for each n×n positive semi‐definite Hermitian matrix A .