FUNDAMENTALS OF INDEX STRUCTURISATION OF NXN-COMBINATORY CONFIGURATIONS

Objectives The aim of the research was to develop a new approach to the configuration formation from the elements of nxn-arrays of sets by the permutations of their elements based on the requirement to order the structures of rows and columns according to the index characteristic.

Methods. The proposed method of "index structurisation" of nxn-arrays of sets is based on the functional dependencies of the index values of the surrounding elements, located directly around any of the elements formed by the configuration permutation, from the index values of the element they surround. The configuration formation from elements of nxn-arrays of sets is carried out by permutations of row and column elements according to given indexing rules and based on the functional dependency of the index values of the surrounding elements from the index values of the element they surround.

Results. A new “index structurisation” approach to the organisation of elemental permutations of information arrays characterising the unique definition of the elements of combinatorial configurations of its structural properties by the rules of indexing, is proposed. General requirements are formulated for the represented functional dependencies of the index values of surrounding elements. The notion of the index remoteness coefficients of surrounding elements is introduced and their influence on the structure of configurations formed is investigated. The properties of the configurations formed by the proposed dependencies as well as the scope of their possible application as discrete system and process models are investigated.

Conclusion. The proposed approach to configuration using permutations of elements of nxn-array of sets, based on the "index structurisation" characterising the unique rules of indexing the elements of combinatorial configurations of its structural properties, establishes a basis for index structurisation of combinatorial configurations.

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