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 -