Geodesic
Nonnegative matrices with zero permanent
Matematičeskie zametki, Tome 58 (1995) no. 4, pp. 493-504

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We study $m\times n$ matrices, $m\ge n$, whose elements are either 1) arbitrary nonnegative numbers or 2) belong to a given finite set of nonnegative numbers that includes zero. In the finite case, we obtain an asymptotic expression, as $n\to\infty$, for the number of matrices with zero permanent. For any nonnegative matrix with zero permanent a standard representation is derived. 
@article{MZM_1995_58_4_a1,
     author = {Yu. V. Bolotnikov and V. E. Tarakanov},
     title = {Nonnegative matrices with zero permanent},
     journal = {Matemati\v{c}eskie zametki},
     pages = {493--504},
     publisher = {mathdoc},
     volume = {58},
     number = {4},
     year = {1995},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1995_58_4_a1/}
}
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Yu. V. Bolotnikov; V. E. Tarakanov. Nonnegative matrices with zero permanent. Matematičeskie zametki, Tome 58 (1995) no. 4, pp. 493-504. http://geodesic.mathdoc.fr/item/MZM_1995_58_4_a1/