On the Polya permanent problem over finite fields

Gregor Dolinar, Alexander E. Guterman, Bojan Kuzma, Marko Orel

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


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.

Original languageEnglish
Pages (from-to)116-132
Number of pages17
JournalEuropean Journal of Combinatorics
Issue number1
StatePublished - Jan 2011
Externally publishedYes


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