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Compositions and samples of geometric random variables with constrained multiplicities

Abstract : We investigate the probability that a random composition (ordered partition) of the positive integer $n$ has no parts occurring exactly $j$ times, where $j$ belongs to a specified finite $\textit{`forbidden set'}$ $A$ of multiplicities. This probability is also studied in the related case of samples $\Gamma =(\Gamma_1,\Gamma_2,\ldots, \Gamma_n)$ of independent, identically distributed random variables with a geometric distribution.
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Margaret Archibald, Arnold Knopfmacher, Toufik Mansour. Compositions and samples of geometric random variables with constrained multiplicities. 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010), 2010, San Francisco, United States. pp.449-460. ⟨hal-01186314⟩

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