Geodesic
Inequalities for the Permanental Minors of Non-Negative Matrices
Canadian journal of mathematics, Tome 18 (1966) no. 1, pp. 608-615

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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. 
Brualdi, R. A.; Newman, M. Inequalities for the Permanental Minors of Non-Negative Matrices. Canadian journal of mathematics, Tome 18 (1966) no. 1, pp. 608-615. doi: 10.4153/CJM-1966-059-5
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[1] 1. Marcus, M. and Gordon, W. R., Inequalities for subpermanents, Illinois J. Math., 8 (1964), 607–614. Google Scholar

[2] 2. Marcus, M. and Newman, M., Inequalities for the permanent function, Ann. Math., 75 (1962), 47–62. Google Scholar

[3] 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] 4. Marcus, M. and Mine, H., A survey of matrix theory and matrix inequalities (Boston, 1964). Google Scholar

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