The Combinatorics of Distributions

Abstract

Distributions, which are the various ways of distributing a certain number of objects of different classes among a collection of targets, have been the subject of combinatorial investigations since MacMahonʼs 1917 monograph. In this paper we apply them to a simulation of superimposed random coding. Furthermore, asymptotic estimates are provided using logarithmic polynomials (related to the well-known Bell polynomials) for symbolic and numeric calculation.