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Journal of the London Mathematical Society 1992 s2-46(1):65-80; doi:10.1112/jlms/s2-46.1.65
© 1992 by London Mathematical Society
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© Oxford University Press

Immanant Inequalities and Partition Node Diagrams

Thomas H. Pate

Mathematics Department (ACA) Math Annex Auburn University Auburn Alabama 36849 USA

If {alpha} is a partition of n then Formula{alpha} denotes the associated normalized immanant. It is shown that if {alpha} = {{alpha}1,...,{alpha}8,...,{alpha}t} is a non-increasing partition of n with {alpha}8 > max {{alpha}8+1, 1} and {alpha}' denotes the partition {{alpha}1,...,{alpha}8–1,...,{alpha}8+1,...{alpha}t, 1} then Formula{alpha}(A) ≥ Formula{alpha}'(A) for each nxn positive semi-definite Hermitian matrix A.


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