Geodesic
Enumeration of permutations with restricted positions and a~fixed number of cycles
Diskretnaya Matematika, Tome 4 (1992) no. 2, pp. 3-22.

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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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     author = {V. S. Shevelev},
     title = {Enumeration of permutations with restricted positions and a~fixed number of cycles},
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     publisher = {mathdoc},
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     number = {2},
     year = {1992},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_1992_4_2_a0/}
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V. S. Shevelev. Enumeration of permutations with restricted positions and a~fixed number of cycles. Diskretnaya Matematika, Tome 4 (1992) no. 2, pp. 3-22. http://geodesic.mathdoc.fr/item/DM_1992_4_2_a0/