Scientific publications

The probabilistic distributions of maximum cell occupancylevels (problem 2) and the numbers of outcomes given their fixed values are studied in models of equiprobable outcomes of the schemes for placing R particles in n cells. The schemes differ in all possible pairwise qualities of cells and particles in terms of their distinguishability. A method for probabilistic analysis of the schemes is proposed, which consists in recalculating the previously obtained results when finding the probabilistic distributions of the minimum cell occupancy levels (problem 1) for certain ratios of their parameters. This technique is based on a specially constructed procedure for coordinated placement of two types of particles of the same quality in terms of distinguishability in the same cells in each scheme studied in problem 2 and its analog with its own number of particles in the scheme studied in problem 1.In this regard, a number of auxiliary novel results were obtained.