Inequalities pp 101-108 | Cite as

Proofs of some Conjectures on Permanents

  • Elliott H. Lieb


In a recent paper [1] Marcus and Minc have given an admirable summary of the theory of permanents of square matrices, especially with regard to inequalities satisfied by the permanent. Our knowledge of permanents is certainly meager compared to that for determinants, largely for the reason that while the former differs from the latter only in the replacement of minus signs by plus signs, the determinant, and not the permanent, is invariant under unitary transformations.


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  1. [1]
    Marvin Marcus & Henry Minc, Permanents, Amer. Math. Monthly, 72 (1965) 577–591.MathSciNetzbMATHCrossRefGoogle Scholar
  2. [2]
    I. Schur, Über endliche Gruppen und Hermitesche Formen, Math. Z., 1 (1918) 184–207.MathSciNetzbMATHCrossRefGoogle Scholar
  3. [3]
    Marvin Marcus, On two classical results of I. Schur, Bull. Amer. Math. Soc., 70 (1964)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Elliott H. Lieb
    • 1
  1. 1.Physics Dept.Northeastern UniversityBostonUSA

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