Enumerative outcome process of a combination scheme.

For the final outcomes of the combination scheme with their fixed probability distribution, an iterative process is developed for their complete repetition-free enumeration, which is represented by an inhomogeneous Markov chain. To this aim we determe the probabilities of its initial states and the transition probabilities (iterative transitions of the process). To calculate this process, we analyze the procedure for compiling a system of equations for them and a general method for solving it (for finding the probabilities of iterative transitions when listing the outcomes of any combinatorial schemes that lead to their desired final probability distribution) with an illustration on an example of a combination scheme with an equiprobable distribution on the set of its outcomes. Based on the process thus constructed, we propose methods for modeling the outcome of the combination scheme both from the result of solving the direct numbering problem and for sequential elementwise modeling of the outcome of the scheme, as the state of a Markov chain. [ABSTRACT FROM AUTHOR]