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On a conjecture of B. L. van der Waerden

Published online by Cambridge University Press:  24 October 2008

Marvin Marcus  and
Henryk Minc
Marvin Marcus
Affiliation:
University of California, Santa Barbara
Henryk Minc
Affiliation:
University of California, Santa Barbara
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Extract

Let Ωn be the set of all n-square doubly stochastic matrices, i.e. matrices with non-negative entries all of whose row sums and column sums are 1. If A = (aij) is an n-square matrix let per (A) denote the permanent of A, that is.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 63 , Issue 2 , April 1967 , pp. 305 - 309
Copyright
Copyright © Cambridge Philosophical Society 1967

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References

REFERENCES

(1)Marcus, M.Some properties and applications of doubly stochastic matrices. Amer. Math. Monthly 67 (1960), 215–221.CrossRefGoogle Scholar
(2)Marcus, M. and Minc, H.Some results on doubly stochastic matrices. Proc. Amer. Math. Soc. 76 (1962), 571–579.CrossRefGoogle Scholar
(3)Marcus, M. and Minc, H.Inequalities for general matrix functions. Bull. Amer. Math. Soc. 70 (1964), 308–313.CrossRefGoogle Scholar
(4)Marcus, M. and Minc, H.A survey of matrix theory and matrix inequalities (Boston, 1964).Google Scholar
(5)Marcus, M. and Minc, H.Generalized matrix functions. Trans. Amer. Math. Soc. 116 (1965), 316–329.CrossRefGoogle Scholar
(6)Marcus, H. and Minc, H.Permanents. Amer. Math. Monthly 72 (1965), 577–591.CrossRefGoogle Scholar
(7)Marcus, M. and Minc, H. Triangle inequalities for generalized matrix functions (submitted for publication).Google Scholar
(8)Marcus, M. and Newman, M.On the minimum of the permanent of a doubly stochastic matrix. Duke Math. J. 26 (1959), 61–72.CrossRefGoogle Scholar
(9)Marcus, M. and Newman, M.Permanents of doubly stochastic matrices. Amer. Math. Soc. Proc. Symp. Appl. Math., vol. 10 (1960), 169–174.CrossRefGoogle Scholar
(10)Marcus, M. and Newman, M.The permanent function as an inner product. Bull. Amer. Math. Soc. 67 (1961), 223–224.CrossRefGoogle Scholar
(11)Marcus, M. and Newman, H.Inequalities for the permanent function. Ann. of Math. 75 (1962), 47–62.CrossRefGoogle Scholar
(12)Minc, H.A note on an inequality of M. Marcus and N. Newman. Proc. Amer. Math. Soc. 14 (1964), 41–46.Google Scholar
(13)Minc, H.Permanents of (0, l)-circulants. Canad. Math. Bull. 7 (1964), 253–263.CrossRefGoogle Scholar
(14)Mirsky, L.Results and problems in the theory of doubly stochastic matrices. Z. Wahrschein. 1 (1963), 319–334.CrossRefGoogle Scholar
(15)Ryser, H. J.Combinatorial mathematics. Carus Math. Monograph no. 14, 1963.Google Scholar
(16)Waerden, B. L.Van Der. Aufgabe 45, Jber. Deutsch. Math. Verein. 35 (1926), 117.Google Scholar