Margaret Archibald ; Arnold Knopfmacher ; Toufik Mansour - Compositions and samples of geometric random variables with constrained multiplicities

dmtcs:2885 - Discrete Mathematics & Theoretical Computer Science, January 1, 2010, DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010) - https://doi.org/10.46298/dmtcs.2885
Compositions and samples of geometric random variables with constrained multiplicitiesArticle

Authors: Margaret Archibald ORCID1; Arnold Knopfmacher ORCID2; Toufik Mansour ORCID3

  • 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.

https://doi.org/10.46298/dmtcs.2885
Source: HAL:hal-01186314v1
Volume: DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010)
Section: Proceedings
Published on: January 1, 2010
Imported on: January 31, 2017
Keywords: multiplicity,Poisson transform,compositions,generating functions,geometric random variable,Mellin transform,[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO],[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

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