Geodesic
Calculation of moments of combinatorial statistics of symmetrically dependent random variables
Diskretnaya Matematika, Tome 17 (2005) no. 2, pp. 3-18 
A. M. Zubkov; D. V. Shuvaev. Calculation of moments of combinatorial statistics of symmetrically dependent random variables. Diskretnaya Matematika, Tome 17 (2005) no. 2, pp. 3-18. http://geodesic.mathdoc.fr/item/DM_2005_17_2_a0/
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Voir la notice de l'article provenant de la source Math-Net.Ru

We consider statistics defined on sequences of symmetrically dependent random variables such that the numbers of ascents, descents, equalities, double ascents, double descents, the number of peaks, and the number of cavities. We obtain explicit expressions for the first moments of such statistics in terms of simple characteristics of the joint distributions. The research of the first author was supported by the program of the President of Russian Federation for support of leading scientific schools, grant 1758.2003.1, and by the program of the Russian Academy of Sciences ‘Modern Problems of Theoretical Mathematics.’

[1] Zubkov A. M., Shuvaev D. V., “Pervye momenty chisla otrezkov neubyvaniya v posledovatelnosti perestanovochnykh sluchainykh velichin”, Obozrenie prikladnoi i promyshlennoi matematiki, 8:2 (2001), 760–761 | MR

[2] Riordan Dzh., Vvedenie v kombinatornyi analiz, IL, Moskva, 1963

[3] Sachkov V. N., Vvedenie v kombinatornye metody diskretnoi matematiki, Nauka, Moskva, 1983 | MR

[4] Yi-Liang Chen, Wei-Hou Cheng, “A note on joint distributions of some random vectors defined on permutations”, Ars Combinatoria, 54 (2000), 139–148 | MR | Zbl