THE PROBABILITY OF SUCCESSFUL ALLOCATION OF PARTICLES IN CELLS (THE GENERAL CASE)

摘要

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.