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Lobachevskii Journal of Mathematics, 2007, Volume 25, Pages 3–7
(Mi ljm1)
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This article is cited in 6 scientific papers (total in 6 papers)
The probability of a successful allocation of ball groups by boxes
F. G. Avkhadiev, A. N. Chuprunov N. G. Chebotarev Research Institute of Mathematics and Mechanics, Kazan State University
Abstract:
Let $p=p_{Nn}$ be the probability of a successful allocation of $n$ groups of distinguishable balls in $N$ boxes in equiprobable scheme for group allocation of balls with the following assumption: each group contains $m$ balls and each box contains not more than $q$ balls from
a same group. If $q=1$, then we easily calculate $p$ and observe that
$p\to e^{-\frac{m(m-1)}2\alpha_0}$ as $n,N\to\infty$ such that $\alpha=\frac nN\to\alpha_0<\infty$. In the case $2\le q$ we also find an explicit formula for the probability and prove that $p\to1$ as $n,N\to\infty$ such that $\alpha=\frac nN\le\alpha'<\infty$.
Keywords:
equiprobable scheme for group allocation of particles, generating function, Cauchy integral.
Received: 24.01.2007
Citation:
F. G. Avkhadiev, A. N. Chuprunov, “The probability of a successful allocation of ball groups by boxes”, Lobachevskii J. Math., 25 (2007), 3–7
Linking options:
https://www.mathnet.ru/eng/ljm1 https://www.mathnet.ru/eng/ljm/v25/p3
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Abstract page: | 650 | Full-text PDF : | 226 | References: | 97 |
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