Composition of numbers with constraints and the hierarchical structure of planar sections of Pascal’s pyramid
- Authors: Kuzmin O.V.1, Strikhar M.V.2,3
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Affiliations:
- Irkutsk State University
- Transbaikal Institute of Railway Transport
- Irkutsk State University of Railway Engineering
- Issue: Vol 234 (2024)
- Pages: 67-74
- Section: Articles
- URL: https://journal-vniispk.ru/2782-4438/article/view/262005
- DOI: https://doi.org/10.36535/2782-4438-2024-234-67-74
- ID: 262005
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Abstract
In this paper, we examine compositions of natural numbers with constraints on natural parts and their relationship with hierarchical combinatorial objects. We derive a formula for calculating the number of such compositions with three constraints based on the sums of elements of planar sections of Pascal’s pyramid. Also, we obtain recurrence relations and generating functions for the numbers of compositions and examine some important special cases for well-known combinatorial numbers.
About the authors
Oleg V. Kuzmin
Irkutsk State University
Author for correspondence.
Email: quzminov@mail.ru
Russian Federation, Irkutsk
Marina V. Strikhar
Transbaikal Institute of Railway Transport; Irkutsk State University of Railway Engineering
Email: mseryogina@mail.ru
Russian Federation, Chita; Irkutsk
References
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