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Inequalities for the Permanental Minors of Non-Negative Matrices

Published online by Cambridge University Press:  20 November 2018

R. A. Brualdi  and
M. Newman
R. A. Brualdi
Affiliation:
National Bureau of Standards, Washington, D.C.
M. Newman
Affiliation:
National Bureau of Standards, Washington, D.C.
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Let A be an n X n non-negative matrix, that is, a matrix whose entries are non-negative numbers. The permanent of A is the scalarvalued function of A defined by

where the summation extends over all permutations i1 … , in of the integers 1, … , n. The purpose of this paper is to prove several inequalities involving the permanent of A and the permanent of submatrices of A when suitable restrictions are placed on the row sums.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 18 , 1966 , pp. 608 - 615
Copyright
Copyright © Canadian Mathematical Society 1966

References

1. Marcus, M. and Gordon, W. R., Inequalities for subpermanents, Illinois J. Math., 8 (1964), 607–614.Google Scholar
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3. Marcus, M. and Newman, M., On the minimum of the permanent of a doubly stochastic matrix, Duke Math. J., 26 (1959), 61–72.Google Scholar
4. Marcus, M. and Mine, H., A survey of matrix theory and matrix inequalities (Boston, 1964).Google Scholar