Central elements in Pascal’s triangle and pyramids: interpretations and relationships
Автор: Kuzmin O.V. , Strikhar M.V.
Журнал: Вестник Бурятского государственного университета. Математика, информатика @vestnik-bsu-maths
Рубрика: Дискретная математика и математическая кибернетика
Статья в выпуске: 2, 2025 года.
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Combinatorial structures, being an integral part of data mod- eling and analysis methodology, enable the creation of modern tools for solving complex problems in various applied fields. This study examines the geometric properties and combinatorial interpretations of the central elements of Pascal’s triangle and pyramid, which represent examples of planar and spatial numerical configurations with hierarchical structures. As a result of the research, a formula generalizing the sum of squares of binomial coefficients was derived based on the geometric and combinato- rial properties of these objects. The proof is founded on the fact that each central element of Pascal’s triangle and pyramid can be interpreted as the number of paths with given initial and terminal points in an integer lattice with unit steps. The main propositions of the work are illustrated by a series of examples.
Pascal’s triangle, Pascal’s pyramid, hierarchical structure, binomial coefficients, trinomial coefficients, central element, numerical sequence, number of paths in integer lattice, sum of squares of binomial coefficients, modeling, data processing, encryption, cryptographic scheme
Короткий адрес: https://sciup.org/148331882
IDR: 148331882 | УДК: 51-7, 519.1 | DOI: 10.18101/2304-5728-2025-2-13-28