On the Polya permanent problem over finite fieldsстатья
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Дата последнего поиска статьи во внешних источниках: 18 июля 2013 г.
Аннотация:Let F be a finite field of characteristics different from two. We show that no
bijective map transforms permanent into determinant when the cardinality of F is
sufficiently large. We also give an example of non-bijective map when F is
arbitrary and an example of a bijective map when F 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.