Geodesic
Variance of the number of cycles of random $A$-permutation
Diskretnaya Matematika, Tome 32 (2020) no. 3, pp. 135-146.

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We consider random permutations having uniform distribution on the set of all permutations of the $n$-element set with lengths of cycles belonging to a fixed set $A$ (so-called $A$-permutations). For some class of sets $A$ the asymptotic formula for the variance of the number of cycles of such permutations is obtained.
Keywords: random $A$-permutations, number of cycles, variance. 
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A. L. Yakymiv. Variance of the number of cycles of random $A$-permutation. Diskretnaya Matematika, Tome 32 (2020) no. 3, pp. 135-146. http://geodesic.mathdoc.fr/item/DM_2020_32_3_a10/

[1] Billingsley P., Convergence of Probability Measures, New York: John Wiley Sons, 1968, xii+253 pp. | MR | Zbl

[2] Bolotnikov Yu. V., Sachkov V. N., Tarakanov V. E., “On some classes of random variables on cycles of permutations”, Math. USSR-Sb., 36:1 (1980), 87–99 | MR | Zbl | Zbl

[3] Goncharov V. L., “On the field of combinatory analysis”, Amer. Math. Soc. Transl., 19 (1962), 1–46 | MR | Zbl | Zbl

[4] Kubilius, J., Probabilistic Methods in the Theory of Numbers, Amer. Math. Soc., Providence, RA, 1964 | MR | Zbl

[5] Kubilius, J., “On the estimate of the second central moment for arbitrary additive arithmetic functions”, Liet. Mat. Rink., 23 (1983), 110–117 | MR

[6] Klimavic̆ius, J., Manstavic̆ius, E., “Turán-Kubilius' inequality on permutations”, Ann. Univ. Sci. Budapest. Sect. Comput., 48 (2018), 45–51 | MR | Zbl

[7] Manstavic̆ius E., Stepas V., “Variance of additive functions defined on random assemblies”, Lith. Math. J., 57:2 (2017), 222–235 | MR | Zbl

[8] Pavlov A. I., “On two classes of permutations with number-theoretic conditions on the lengths of the cycles”, Math. Notes, 62:6 (1997), 739–746 | MR | Zbl

[9] Sachkov V.N., Vvedenie v kombinatornye metody diskretnoi matematiki, MTsNMO, Moskva, 2004, 424 pp.

[10] Turán, P., “Uber Einige Verallgemeinerungen Eines Satzes von Hardy und Ramanujan”, J. London Math. Soc., 11:2 (1936), 125—133 | MR

[11] Yakymiv A. L., “Asymptotics of the moments of the number of cycles of a random $A$-permutation”, Math. Notes, 88:5 (2010), 759–766 | MR | Zbl

[12] Yakymiv A. L., “Asimptotika momentov chisla tsiklov sluchainoi $A$-podstanovki s ostatochnym chlenom”, Diskretnaya matematika, 31:3 (2019), 114—127 | MR