On the Polya permanent problem over finite fields

Details On the Polya permanent problem over finite fields On the Polya permanent problem over finite fields

2010-03-09

arxiv.org/abs/1003.1984v1

Mathematics

Combinatorics

25 pages

Scientific paper

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

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