S-restricted compositions revisited

Behrouz Zolfaghari, M. S. Fallah*, Mehdi Sedighi

*この研究の対応する著者

研究成果: Article査読

抄録

An S-restricted composition of a positive integer n is an ordered partition of n where each summand is drawn from a given subset S of positive integers. There are various problems regarding such compositions which have received attention in recent years. This paper is an attempt at finding a closed-form formula for the number of S-restricted compositions of n. To do so, we reduce the problem to finding solutions to corresponding so-called interpreters which are linear homogeneous recurrence relations with constant coefficients. Then, we reduce interpreters to Diophantine equations. Such equations are not in general solvable. Thus, we restrict our attention to those S-restricted composition problems whose interpreters have a small number of coefficients, thereby leading to solvable Diophantine equations. The formalism developed is then used to study the integer sequences related to some well-known cases of the S-restricted composition problem.

本文言語English
論文番号9
ジャーナルDiscrete Mathematics and Theoretical Computer Science
19
1
出版ステータスPublished - 2017
外部発表はい

ASJC Scopus subject areas

  • 理論的コンピュータサイエンス
  • コンピュータ サイエンス(全般)
  • 離散数学と組合せ数学

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