Abstract
We studym×n matrices,m≤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, asn → ∞, for the number of matrices with zero permanent. For any nonnegative matrix with zero permanent a standard representation is derived.
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References
W. Feller,An Introduction to Probability Theory and its Applications, Vol. 1, J. Wiley, New York (1950).
P. Erdös and A. Rényi, “On random matrices,”Magyar Tud. Akad. Mat. Kutató Int. Közl.,8, 455–461 (1963).
V. N. Sachkov,Probability Methods in Combinatorial Analysis [in Russian], Nauka, Moscow (1978).
T. I. Fenner and G. Loizou, “Combinatorial aspects of rectangular nonnegative matrices,”Discrete Math.,20, No. 3, 217–234 (1977/78).
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Translated fromMatematicheskie Zametki, Vol. 58, No. 4, pp. 493–504, October, 1995.
This work was partially supported by the Russian Foundation for Basic Research under grant No. 93-011-1443.
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Bolotnikov, Y.V., Tarakanov, V.E. Nonnegative matrices with zero permanent. Math Notes 58, 1021–1028 (1995). https://doi.org/10.1007/BF02305089
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DOI: https://doi.org/10.1007/BF02305089