Geometric models of combinatorial identities

- Даниліна, Г.В. (orcid.org/0009-0007-3634-7734), Рашевський, М.О. (orcid.org/0000-0003-1136-2691) and Семеріков, С.О. (orcid.org/0000-0003-0789-0272) (2024) Geometric models of combinatorial identities Математичне моделювання, 1 (50). pp. 32-40. ISSN 2519-8106

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Abstract

The method of trajectories appeared in the work of D. Andre, where the reflection method was applied to the Bertrand’s ballot problem. In the works of B.V. Gnedenko and his colleagues, the method of trajectories was applied to problems of mathematical statistics. The method of trajectories in combinatorics and probability theory is to reduce problems to counting paths on integer lattices. The proof of combinatorial identities by the method of trajectories consists in calculating the shortest lattice paths in two ways. In this paper, we propose a spatial version of the trajectory method and apply it to the proof of combinatorial identities. Generalizations of known combinatorial identities and proofs of new ones are considered. Several combinatorial identities are proved using a spatial coordinate system. On the other hand, due to its visualization, the trajectory method can also be used in teaching combinatorial math. Visualization of educational material is a very important component of the teaching methodology. Increasing the dimensionality reduces the visibility of the material, but positively affects the ability to logically analyze problems. Further research could be aimed at building trajectories in a more dimensional space and visualizing them.

Item Type:	Article
Keywords:	combinatorial structures, combinatorial identities, trajectories, visualization, teaching math
Subjects:	Science and knowledge. Organization. Computer science. Information. Documentation. Librarianship. Institutions. Publications > 5 Мathematics. natural sciences > 51 Mathematics
Divisions:	Institute for Digitalisation of Education > Department of Cloud-Oriented Systems and Artificial Intelligence in Education
Depositing User:	Сергій Олексійович Семеріков
Date Deposited:	21 Jul 2024 10:51
Last Modified:	21 Jul 2024 10:51
URI:	https://lib.iitta.gov.ua/id/eprint/741786

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