Geodesic
Description of the class of permutations, represented as a~product of two permutations with fixed number of mobile points
Prikladnaâ diskretnaâ matematika, no. 13 (2011), pp. 16-17

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The structure of the class of permutations represented as the product of two permutations with $q$ mobile points, $4\le q\le N/2$, is completely described. 
@article{PDM_2011_13_a6,
     author = {A. B. Pichkur},
     title = {Description of the class of permutations, represented as a~product of two permutations with fixed number of mobile points},
     journal = {Prikladna\^a diskretna\^a matematika},
     pages = {16--17},
     publisher = {mathdoc},
     number = {13},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDM_2011_13_a6/}
}
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A. B. Pichkur. Description of the class of permutations, represented as a~product of two permutations with fixed number of mobile points. Prikladnaâ diskretnaâ matematika, no. 13 (2011), pp. 16-17. http://geodesic.mathdoc.fr/item/PDM_2011_13_a6/