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The Probability of Successful Allocation of Particles in Cells (The General Case)

Abstract

Let p nN be the probability of successful allocation of n groups of particles in N cells with the following assumptions: (a) each group contains m particles and has allocation as a general allocation scheme; (b) each cell contains at most r particles from the same group; (c) events connected with different groups are independent. We obtain an asymptotically exact bound of p nN as n,N →∞ such that n/N is bounded. Applications to problems in error-correcting coding are considered.

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Correspondence to I. R. Kayumov.

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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 18, No. 5, pp. 119–128, 2013.

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Kayumov, I.R., Chuprunov, A.N. The Probability of Successful Allocation of Particles in Cells (The General Case). J Math Sci 209, 88–95 (2015). https://doi.org/10.1007/s10958-015-2486-2

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Keywords

  • Allocation Scheme
  • Root Vertex
  • Distinguishable Particle
  • Nonroot Vertex
  • Oriented Contour