Geodesic
On the Permanent of a Doubly Stochastic Matrix
Canadian journal of mathematics, Tome 18 (1966) no. 1, pp. 758-761

Voir la notice de l'article provenant de la source Cambridge University Press

If is an n X n matrix, the permanent of A, Per A, is defined by 1 where the sum is over all permutations. If A is doubly stochastic (i.e., nonnegative with row and column sums all equal to 1), then it has been conjectured that Per A ⩾ n!/nn . When confronted with a vaguely similar problem about determinants, M. Kac (1) observed that the computation of minima can often be aided by knowledge of various averages. In this spirit we calculate here the average permanent of a class of doubly stochastic matrices and thereby obtain upper bounds for the minima. These turn out to be surprisingly sharp. 
Wilf, Herbert S. On the Permanent of a Doubly Stochastic Matrix. Canadian journal of mathematics, Tome 18 (1966) no. 1, pp. 758-761. doi: 10.4153/CJM-1966-076-6
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[1] 1. Kac, M., Probability and related topics in physical sciences, Seminar at Boulder, Colorado, Summer, 1957 (lecture notes). Google Scholar

[2] 2. Nikolai, P. J., Permanents of incidence matrices, MTAC(1960), 262–266. Google Scholar

[3] 3. Ryser, H. J., Matrices of zeros and ones, Bull. Amer. Math. Soc, 66 (1960), 442–464. Google Scholar

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