RULES FOR DEVELOPING SIGNIFICANT COMBINARY SPACES

Abstract

Significant combinatorial spaces exist in two states: tranquility (convolute), which is given by the sign, and dynamics (deployed), which deployed from convolute. The points of these spaces are combinatorial configurations of different types. Their construction is based on the rules of formation and ordering of these objects. The latter are formed from the elements of a given basic set by three recurrent combinatorial operators, and are ordered according to the rules in which the periodicity property is used. The significant convolute combinatorial space is given by an information sign, which contains the base set, its type and rules of formation from the elements of the base set of points of the deployed space. In nature, there are a finite number of sets of combinatorial configurations of the same type, each of which can be ordered in different ways, both strictly and chaotically. As the analysis of these sets has shown, many of them are ordered by the same strict procedures, ie there are patterns of their generation. One of them is the property of periodicity, which follows from the recurrent method of formation and ordering of combinatorial configurations. Based on this property, a recurrent-periodic method was developed, focused on generating combinatorial configurations of different types. Using this method, the ordering of structured combinatorial sets is performed according to the same rules, and some of them are generated by different modifications of the same algorithm. The article describes the rules of formation and ordering of structured combinatorial sets and, respectively, sign combinatorial spaces. Three recurrent combinatorial operators are introduced, according to which combinatorial configurations are formed. It is a transposition, a selection, and an arithmetic operator. Three rules are formulated according to which combinatorial sets are ordered. These rules are formed on the basis of the analysis of their structure. The generation of combinatorial sets is performed from the elements of a given base set using the above rules. That is, for their generation it is enough to specify the type of combinatorial configuration, the base set and the rules of their formation and ordering. The significant combinatorial space is similarly described.