Geodesic
Variance of the additive weight deficit of equiprobable involution on the residue group
Matematičeskie voprosy kriptografii, Tome 10 (2019) no. 3, pp. 101-116 Cet article a éte moissonné depuis la source Math-Net.Ru

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We find exact and asymptotic formulas for the variance of the random variable $\zeta_n$ which is equal to the weight deficit of random involution defined on the additive group of residues modulo natural number $n$. The asymptotic formula for $n\to\infty$ has the following form: $$ \mathbf{D}{{\zeta}_{n}}=n\left(e^{-\frac{1}{2}}-\frac{3}{2}{{e}^{-1}} \right)\left(1+O\left(\frac{1}{n^{\frac{1}{3}}} \right) \right). $$ 
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     author = {V. N. Sachkov and I. A. Kruglov},
     title = {Variance of the additive weight deficit of equiprobable involution on the residue group},
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V. N. Sachkov; I. A. Kruglov. Variance of the additive weight deficit of equiprobable involution on the residue group. Matematičeskie voprosy kriptografii, Tome 10 (2019) no. 3, pp. 101-116. http://geodesic.mathdoc.fr/item/MVK_2019_10_3_a6/

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[2] Sachkov V. N., Kruglov I. A., “Vesovye defitsity involyutsii i podstanovok”, Matematicheskie voprosy kriptografii, 7:4 (2016), 95–116 | DOI | MR

[3] Sachkov V. N., “Involyutsii s dannym vesovym defitsitom, sootvetstvuyuschie tablitse Keli konechnoi abelevoi gruppy”, Matematicheskie voprosy kriptografii, 8:4 (2017), 117–134 | DOI | MR

[4] Sachkov V. N., Kruglov I. A., “Momenty vesovogo defitsita sluchainoi ravnoveroyatnoi involyutsii, deistvuyuschei na konechnom vektornom prostranstve nad polem iz dvukh elementov”, Matematicheskie voprosy kriptografii, 9:4 (2018), 101–124 | DOI | MR

[5] Sachkov V. N., Kurs kombinatornogo analiza, NITs «Regulyarnaya i khaoticheskaya dinamika», Moskva–Izhevsk, 2013, 336 pp.