Abstract:
A general algorithm for enumerating permutations with bounded positions and a fixed number of cycles has been obtained, apparently for the first time, with the help of the cyclic polynomial (or cycloment), introduced in the article, for a square matrix. The obtained algorithm can be used for parallel computation of the permanent and determinant of a matrix, as well. For Toeplitz matrices, a coefficients method for computing the cycloment has been developed. Besides, cycloments of some other matrices of order $n$ have been computed.
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