Abstract
New algorithms for calculating exact analytical dependences arising in the solution of various theoretical and applied problems related to the analysis of random point structures are proposed, substantiated and implemented. New scientific results presented in this work were obtained using original research methods based on computer analytics programs using generalized multidimensional Catalan numbers. Предложены, обоснованы и программно реализованы новые алгоритмы расчета точных аналитических зависимостей, возникающих при решении различных теоретических и прикладных задач, связанных с анализом случайных точечных структур. Отличительной особенностью работы является то, что достигнутые в ней новые научные результаты получены с помощью оригинальных методов исследования на основе программ компьютерной аналитики с использованием обобщенных многомерных чисел Каталана.
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