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Bounds for permanents of non-negative matrices1

Published online by Cambridge University Press:  20 January 2009

Henryk Minc
Henryk Minc
Affiliation:
University of California, Santa Barbara, California
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Let v = (a1 …, an) be a real n-tuple and be the numbers a1 …, an arranged in decreasing order. Let denote the sum of m greatest components of v and the sum of m smallest components of v, i.e.,

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 16 , Issue 3 , June 1969 , pp. 233 - 237
Copyright
Copyright © Edinburgh Mathematical Society 1969

References

REFERENCES

(1)Jurkat, W. B. and Ryser, H. J.Matrix factorizations of determinants and permanents, J. of Algebra, 3 (1966), 1–27.CrossRefGoogle Scholar
(2)Marcus, M. and Minc, H.A survey of matrix theory and matrix inequalities (Boston, 1964).Google Scholar
(3)Marcus, M. and Minc, H.Permanents, Amer. Math. Monthly, 72 (1965), 577–591.CrossRefGoogle Scholar
(4)Marcus, M. and Minc, H.On a conjecture of B. L. van der Waerden, Proc. Cambridge Phil. Soc. 63 (1967), 305–309.CrossRefGoogle Scholar
(5)Minc, H.A lower bound for permanents of (0, l)-matrices, Proc. Amer. Math. Soc, 18 (1967), 1128–1132.Google Scholar