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Immanant Inequalities and Partition Node Diagrams
Author(s) -
Pate Thomas H.
Publication year - 1992
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/s2-46.1.65
Subject(s) - partition (number theory) , mathematics , hermitian matrix , combinatorics , discrete mathematics , pure mathematics
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 .