Geodesic
Permanents of Random Doubly Stochastic Matrices
Canadian journal of mathematics, Tome 26 (1974) no. 3, pp. 600-607

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The permanent of an n × n matrix A = (aij ) is defined as where Sn is the symmetric group of order n. For a survey article on permanents the reader is referred to [2]. An unresolved conjecture due to van der Waerden states that if A is an n × n doubly stochastic matrix; then per (A) ≧ n!/nn , with equality if and only if A = Jn = (1/n). 
Griffiths, R. C. Permanents of Random Doubly Stochastic Matrices. Canadian journal of mathematics, Tome 26 (1974) no. 3, pp. 600-607. doi: 10.4153/CJM-1974-057-4
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[1] 1. Marcus, M., Inequalities for matrix functions of combinatorial interest, SIAM J. Appl. Math. 17 (1969), 1023–1031. Google Scholar

[2] 2. Marcus, M. and Minc, H., Permanents, Amer. Math. Monthly 72 (1965), 577–591. Google Scholar

[3] 3. Ryser, H. R., Combinatorial mathematics, No. 14 of the Carus Mathematical Monographs, the Mathematical Association of America, 1963. Google Scholar

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