The probability of successful allocation of particles in cells (the general case)

Abstract

© 2015, Springer Science+Business Media New York. Let p<inf>nN</inf> 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<inf>nN</inf> as n,N →∞ such that n/N is bounded. Applications to problems in error-correcting coding are considered.