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<p>In this paper, we propose an algorithm for enumerating and calculating compositions of a natural number based on combinatorial objects of a hierarchical structure, such as the Pascal triangle, the Pascal pyramid, and the Pascal hyperpyramids. We obtain a recurrent relation that is the basis for enumerating and calculating compositions of a natural number with an arbitrary constraints on the values of its natural parts and the formula for explicit calculating compositions and a generating function for the number of compositions.</p>

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COMBINATORIAL ALGORITHM FOR ENUMERATING AND CALCULATING COMPOSITIONS OF NATURAL NUMBERS WITH CONSTRAINTS

  • 期刊论文

  • 发表日期：

    2025年8月1日

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  • O. Kuzmin,
  • M. Strikhar

摘要

In this paper, we propose an algorithm for enumerating and calculating compositions of a natural number based on combinatorial objects of a hierarchical structure, such as the Pascal triangle, the Pascal pyramid, and the Pascal hyperpyramids. We obtain a recurrent relation that is the basis for enumerating and calculating compositions of a natural number with an arbitrary constraints on the values of its natural parts and the formula for explicit calculating compositions and a generating function for the number of compositions.