Authors: Margaret Archibald ¹; Arnold Knopfmacher ²; Toufik Mansour ³

• 1 Laboratory of Foundational Aspects of Computer Science
• 2 The John Knopfmacher Centre for Applicable Analysis and Number Theory [Johannesburg]
• 3 Department of Mathematics [Haïfa]

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.