Geodesic
The number of matrices with nonzero permanent over a~finite field
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXX, Tome 463 (2017), pp. 13-24

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A new method for obtaining lower bounds on the number of matrices over a finite field with nonzero permanent is developed. Some earlier results are improved. 
@article{ZNSL_2017_463_a1,
     author = {M. V. Budrevich},
     title = {The number of matrices with nonzero permanent over a~finite field},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {13--24},
     publisher = {mathdoc},
     volume = {463},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2017_463_a1/}
}
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M. V. Budrevich. The number of matrices with nonzero permanent over a~finite field. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXX, Tome 463 (2017), pp. 13-24. http://geodesic.mathdoc.fr/item/ZNSL_2017_463_a1/