ИСТИНА

This is a joint work with Mikhail Budrevich, Gregor Dolinar, Bojan Kuzma and Marko Orel. Two important functions in matrix theory, determinant and permanent, look very similar: $$ \det A= \sum_{\sigma\in { S}_n} (-1)^{\sigma} a_{1\sigma(1)}\cdots a_{n\sigma(n)} \quad \mbox{ and } \quad \per A= \sum_{\sigma\in { S}_n} a_{1\sigma(1)}\cdots a_{n\sigma(n)} $$ here $A=(a_{ij})\in M_n(\F)$ is an $n\times n$ matrix and ${ S}_n$ denotes the set of all permutations of the set $\{1,\ldots, n\}$. While the computation of the determinant can be done in a polynomial time, it is still an open question, if there are such algorithms 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. The lecture will contain the exposition of this theory during the past 100 years including our recent research results in this topic.