Abstract
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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References
Marvin Marcus & Henry Minc, Permanents, Amer. Math. Monthly, 72 (1965) 577–591.
I. Schur, Über endliche Gruppen und Hermitesche Formen, Math. Z., 1 (1918) 184–207.
Marvin Marcus, On two classical results of I. Schur, Bull. Amer. Math. Soc., 70 (1964)
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© 2002 Springer-Verlag Berlin Heidelberg
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Lieb, E.H. (2002). Proofs of some Conjectures on Permanents. In: Loss, M., Ruskai, M.B. (eds) Inequalities. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-55925-9_11
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DOI: https://doi.org/10.1007/978-3-642-55925-9_11
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