For a set of n discernible objects, the probability of choosing at random a permutation with m objects fixed is determined with the help of the generating function method. It is shown that the expected number of objects left fixed is one, which represents a special interpretation of Burnside's Lemma. Furthermore, the higher moments about the origin are represented by Stirling's numbers of the second kind, or simpler, by Bell's numbers, and the factorial moments are all one. A short discussion of an estimation problem concludes the paper.
Montmorto uždavinys, Bernsaido lema ir Belo skaičiai
Darbe nagrinėjami klasikiniai kombinatorikos uždaviniai su tam tikra tikimybine interpretacija. Autorius taiko generuojančių funkcijų metodą ivairiems momentams skaičiuoti. Kai kurios iš įrodomų straipsnyje formulių nėra gerai žinomos kombinatorinėje analizėje. Kaip atskiri šių formulių rezultatai gaunami klasikiniai Stirlingo ir Belo skaičių saryšiai. Straipsnyje pareikta trumpa nagrinėjamų uždavinių apžvalga.
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