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Article

Анализ схемы размещения неразличимых частиц по неразличимым ячейкам

Энатская Н.Ю., Хакимуллин Е. Р., Колчин А. В.

The following investigations are carried out in the general scheme of allocation of indistinguishable particles to indistinguishable cells and in the particular scheme with no empty cell allowed. A recurrence relation is found for the total number of outcomes of the particular scheme and an explicit expression for it is obtained. A relation between the numbers of outcomes of the general and particular schemes is found. A random process of successive allocation of a single particle to cells which provides us with an algorithm for solving the combinatorial problem and finding all the outcomes of allocation of a fixed number of particles to cells in the scheme under consideration and finding the distribution of their probabilities is escribed. Various methods to simulate the states of the scheme and approximate the numberof its outcomes by means of stochastic simulation techniques are suggested.