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The article considers the sport legislation codification project viewed as an effective tool to counter many negative trends in the national sports due to the deficiencies of the valid sport legislation and drawbacks of the existing sport self-regulation system. The article gives grounds for the urgent and significant homologation (i.e. improvement of an object or process with its key characteristics being put in compliance with the relevant standards/requirements, with the path to the compliance being specified) of the Russian sport legislation via its codification; with a special emphasis on homologation of the national autonomous off-/extra-legal regulatory standards in the sport sector. We believe that the proposed initiatives are highly necessary for the progress of the national sports. A top priority in the newly designed legal doctrine for the sport sector must be given to the notion of order as identifying the degree of order/entropy in the subject sector. The illusions as to the government ability to control the sport sector are more and more diminished, and the sport sector resistance to the governmental control efforts tends to grow. It is the codification that may provide a set of proved tools for the large-scale homologation of the relevant legislative domain and integrated regulation of the sector. The study gives definitions of a few notions including order, autonomous extra-legal regulatory order in the sport sector, and the sport legislation codification. It is noted that the sport legislation codification (viewed as a vehicle for the homologation of order in the sport sector) may largely mitigate the current problems faced by the national sport sector, contribute to the dignity of the Russian sports and improve their image on the global arenas.

The paper introduces the concept of generalized Catalan numbers as a useful tool for solving many theoretical and applied combinatorial-probabilistic problems. Combined with analytical transformation software algorithms, the generalized Catalan numbers simplify the solution of many problems in computer science and applied mathematics. In particular, they turn out to be an effective tool for solving problems related to the registration of random-dot images, in signal transformations of various degrees of smoothness, and when developing speed-optimal algorithms for searching for pulsed-point objects with a random generation time of super short pulses. The proposal of the authors to formulate the problems of enumerative combinatorics in a word-symbolic form naturally leads to multidimensional extensions of the classical Catalan numbers and has several advantages. The combined use of multidimensional Catalan numbers and high-performance computer algebra systems enables solving a number of complex applied problems related to the reliability of the registration of random-dot images.

The paper discusses an approach to solving complex probabilistic combinatorial problems. The approach is based on the use of specialized software systems for analytical transformations for computing systems. One of the problems associated with the partition of the interval (which arises in the study of the reliability of reading discrete-point fields and digital images) is considered in the paper, and new previously unknown analytical formulas have been successfully obtained. The efficiency of the developed software systems is ensured by two factors: firstly, the development of high-speed specialized recursive-combinatorial algorithms; secondly, the software implementation on high-performance computing clusters using modern programming and development tools (such as C ++ and MPI).
Examples of particular solutions to the described problem that are obtained with the help of constructed computer systems are presented. An effective approach to solving complex probabilistic combinatorial problems is demonstrated. For the proposed approach, a computer is not just a powerful "calculator", but is an effective assistant with a wide range of algorithms and programs for complex and branched analytical transformations.