Geodesic
Composition of numbers with constraints and the hierarchical structure of planar sections of Pascal's pyramid
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the 5th International Conference "Dynamical Systems and Computer Science: Theory and Applications" (DYSC 2023). Irkutsk, September 18-23, 2023, Tome 234 (2024), pp. 67-74

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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.
Keywords: composition of number, hierarchical structure, recurrence relation, generating function, Tribonacci numbers, Fibonacci numbers
Mots-clés : Pascal's pyramid, Pascal's triangle 
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     title = {Composition of numbers with constraints and the hierarchical structure of planar sections of {Pascal's} pyramid},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
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O. V. Kuz'min; M. V. Strihar. Composition of numbers with constraints and the hierarchical structure of planar sections of Pascal's pyramid. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the 5th International Conference "Dynamical Systems and Computer Science: Theory and Applications" (DYSC 2023). Irkutsk, September 18-23, 2023, Tome 234 (2024), pp. 67-74. http://geodesic.mathdoc.fr/item/INTO_2024_234_a8/