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Article

Метод графов для решения задач перечислительной комбинаторики

Энатская Н. Ю., Хакимуллин Е. Р.

The possibilities of research of combinatorial circuits of particles in cells based on graphs of stochastic processes in the respective schemes poedinichnom adding particles with a specific numbering at each step to organize easily calculable probabilities. Such information enables precise probabilistic analysis of interest layouts. The essence of the method consists in constructing a graph of a random process with poedinichnom adding particles in the combinatorial circuit in all possible ways with certain distinct discipline their numbering in the corresponding graph states. Number of process steps defined in the schema specify the total number of particles placed. We are interested in the list of all the states, and, hence, their number on, the last step. If on, the edges of the graph indicate the probability of all transitions with standing in state at any step of the process, given its properties, the probability of all outcomes scheme calculated by the formulas of addition and multiplication of probabilities and give full information about the process, allowing to conduct further analysis of the scheme. Therefore, the immediate goal of research of combinatorial circuits is to get all of their probability distributions explicitly listed outcomes. A first problem will be solved enumerative combinatorics for all outcomes of interest combinatorial circuits.