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 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

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},
     year = {2017},
     volume = {463},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2017_463_a1/}
}
TY  - JOUR
AU  - M. V. Budrevich
TI  - The number of matrices with nonzero permanent over a finite field
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2017
SP  - 13
EP  - 24
VL  - 463
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2017_463_a1/
LA  - ru
ID  - ZNSL_2017_463_a1
ER  - 
%0 Journal Article
%A M. V. Budrevich
%T The number of matrices with nonzero permanent over a finite field
%J Zapiski Nauchnykh Seminarov POMI
%D 2017
%P 13-24
%V 463
%U http://geodesic.mathdoc.fr/item/ZNSL_2017_463_a1/
%G ru
%F ZNSL_2017_463_a1
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/

[1] V. N. Sachkov, V. E. Tarakanov, Kombinatorika neotritsatelnykh matrits, Nauchnoe izdatelstvo TPV, M., 2000 | MR

[2] L. A. Bassalygo, “On the number of nonzero permanents over a finite field of odd characteristic”, Probl. Inform. Transm., 49:4 (2013), 382–83 | DOI | MR

[3] R. A. Brualdi, H. J. Ryser, Combinatorial Matrix Theory, Cambridge Univ. Press, 1991 | MR | Zbl

[4] M. V. Budrevich, A. E. Guterman, “Permanent has less zeros than determinant over finite fields”, Contemp. Math., 579 (2012), 33–42 | DOI | MR | Zbl

[5] S. A. Cook, “The complexity of theorem proving procedures”, Proc. 3rd Ann. ACM Symp. Theory of Computing, 1971, 151–158 | Zbl

[6] G. Dolinar, A. Guterman, B. Kuzma, M. Orel, “On the Pólya permanent problem over finite fields”, Eur. J. Comb., 32 (2011), 116–132 | DOI | MR | Zbl

[7] M. A. Duffner, H. F. da Cruz, “A relation between the determinant and the permanent on singular matrices”, Linear Algebra Appl., 438 (2013), 3654–3660 | DOI | MR | Zbl

[8] M. R. Garey, D. S. Johnson, Computers and Intractability: A Guide to the Theory of $NP$-Completness, W. H. Freeman, San Francisco, 1979 | MR

[9] R. M. Karp, “Reducibility among combinatorial problems”, Complexity of Computer Computations, Plenum Press, New York, 1972, 85–104 | DOI | MR

[10] L. G. Valiant, “The complexity of computing the permanent”, Theor. Comput. Sci., 8 (1979), 189–201 | DOI | MR | Zbl

[11] W. McCuaig, “Pólya's permanent problem”, Electron. J. Combin., 11 (2004), Research Paper 79 | MR | Zbl

[12] H. Minc, Permanents, Addison-Wesley Publishing Company, Inc, 1978 | MR | Zbl

[13] V. V. Vazirani, M. Yannakakis, “Pfaffian orientations, 0-1 permanents, and even cycles in directed graphs”, Discrete Appl. Math., 25 (1989), 179–190 | DOI | MR | Zbl