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. 
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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/

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