TY - JOUR

T1 - On the Polya permanent problem over finite fields

AU - Dolinar, Gregor

AU - Guterman, Alexander E.

AU - Kuzma, Bojan

AU - Orel, Marko

PY - 2011/1

Y1 - 2011/1

N2 - Let F be a finite field of characteristic different from 2. We show that no bijective map transforms the permanent into the determinant when the cardinality of F is sufficiently large. We also give an example of a non-bijective map when F is arbitrary and an example of a bijective map when F is infinite which do transform the permanent into the determinant. The technique developed allows us to estimate the probability of the permanent and the determinant of matrices over finite fields having a given value. Our results are also true over finite rings without zero divisors.

AB - Let F be a finite field of characteristic different from 2. We show that no bijective map transforms the permanent into the determinant when the cardinality of F is sufficiently large. We also give an example of a non-bijective map when F is arbitrary and an example of a bijective map when F is infinite which do transform the permanent into the determinant. The technique developed allows us to estimate the probability of the permanent and the determinant of matrices over finite fields having a given value. Our results are also true over finite rings without zero divisors.

UR - http://www.scopus.com/inward/record.url?scp=77957790501&partnerID=8YFLogxK

U2 - 10.1016/j.ejc.2010.07.001

DO - 10.1016/j.ejc.2010.07.001

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AN - SCOPUS:77957790501

SN - 0195-6698

VL - 32

SP - 116

EP - 132

JO - European Journal of Combinatorics

JF - European Journal of Combinatorics

IS - 1

ER -