Geodesic
Description of the class of permutations represented as a~product of two permutations with fixed number of mobile points.~II
Prikladnaya Diskretnaya Matematika. Supplement, no. 5 (2012), pp. 21-22.

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The complete description for the structure of the class of permutations represented as the product of two permutations with $q$ and $q+t$ mobile points is given in the case $1\le t$, $2\le q(N-t)/2+1$. 
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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.~II. Prikladnaya Diskretnaya Matematika. Supplement, no. 5 (2012), pp. 21-22. http://geodesic.mathdoc.fr/item/PDMA_2012_5_a9/

[1] Pichkur A. B., “Opisanie klassa podstanovok, predstavimykh v vide proizvedeniya dvukh podstanovok s fiksirovannym chislom mobilnykh tochek”, Prikladnaya diskretnaya matematika. Prilozhenie, 2011, no. 4, 16–17