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A New Algorithm for Computing the Frobenius Number | ||
| Journal of Algorithms and Computation | ||
| دوره 56، شماره 2، اسفند 2024، صفحه 68-74 اصل مقاله (477.95 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22059/jac.2025.372565.1211 | ||
| نویسندگان | ||
| Abbas Taheri1؛ Saeid Alikhani* 2 | ||
| 1Department of Electrical Engineering, Yazd University, 89195-741, Yazd, Iran | ||
| 2Department of Mathematical Sciences, Yazd University, 89195-741, Yazd, Iran | ||
| چکیده | ||
| A number $\alpha$ has a representation with respect to the numbers $\alpha_1,...,\alpha_n$, if there exist the non-negative integers $\lambda_1,... ,\lambda_n$ such that $\alpha=\lambda_1\alpha_1+...+\lambda_n \alpha_n$. The largest natural number that does not have a representation with respect to the numbers $\alpha_1,...,\alpha_n$ is called the Frobenius number and is denoted by the symbol $g(\alpha_1,...,\alpha_n)$. In this paper, we present a new algorithm to calculate the Frobenius number. Also we present the sequential form of the new algorithm. A number $\alpha$ has a representation with respect to the numbers $\alpha_1,...,\alpha_n$, if there exist the non-negative integers $\lambda_1,... ,\lambda_n$ such that $\alpha=\lambda_1\alpha_1+...+\lambda_n \alpha_n$. The largest natural number that does not have a representation with respect to the numbers $\alpha_1,...,\alpha_n$ is called the Frobenius number and is denoted by the symbol $g(\alpha_1,...,\alpha_n)$. In this paper, we present a new algorithm to calculate the Frobenius number. Also we present the sequential form of the new algorithm. | ||
| کلیدواژهها | ||
| Algorithm؛ Frobenius؛ Number؛ Complexity؛ Sequence | ||
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