ИСТИНА

The talk is based on the works [1, 2, 3]. While the computation of the determinant can be done in a polynomial time, it is still an open question, if there exists a polynomial algorithm to compute the permanent. Due to this reason, starting from the work by P\'olya, 1913, different approaches to convert the permanent into the determinant were under the intensive investigation. Among our results we prove the following theorem: Theorem 1. Suppose $n\ge 3$, and let $ F$ be a finite field with ${\rm char}\, F \ne2$. Then, no bijective map $T:M_n( F)\to M_n(F)$ satisfies ${\rm per}\, A=\det T(A).$ [1] M. Budrevich, A. Guterman: Permanent has less zeros than determinant over finite fields, {\em American Mathematical Society, Contemporary Mathematics,\/} {\bf 579}, (2012) 33-42. [2] A.Guterman, G.Dolinar, B.Kuzma, P\'olya's convertibility problem for symmetric matrices, {\em Mathematical Notes,\/} {\bf 92}, no. 5, (2012) 684-698. [3] G. Dolinar, A. Guterman, B. Kuzma, M. Orel, On the P\'olya's permanent problem over finite fields, {\em European Journal of Combinatorics\/}, {\bf 32} (2011) 116-132.