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Article

Анализ схемы равновероятного размещения различимых частиц по неразличимым ячейкам

Н. Ю. Энатская, Е. Р. Хакимуллин

The primal problem of research consists in finding of number of outcomes of the studied scheme and their transfer in an explicit form. The form of representation of outcomes is for this purpose discussed. On the basis of comparison with the similar scheme with indiscernible particles studied in [1] with the found number of outcomes of S the apparent formula for number of outcomes of N these schemes expressed through S is removed.

Along with rather laborious analytical calculation of number of outcomes of the scheme N, the assuming preliminary finding of number S on [1], is offered a numerical method of definition of N at any fixed values of parameters of the scheme (n – numbers of cells and r – number of particles) by creation of a state graph of casual process of poyedinichny serial placement of particles on cells to r-oho step with particular discipline of numbering of the states describing scheme outcomes in the taken form. On the same count with the indication of easily calculated probabilities of transitions from a state to a state procedure of calculation of probability distribution of outcomes of the scheme after placement of the fixed number of particles is offered. Thus, we receive the complete list of all outcomes of the scheme and their probability distribution. Besides, the numerical method of approximate calculation of number of outcomes of the scheme is given by method of stochastic model operation. Questions of model operation of outcomes of the scheme are also considered.