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Dal'nevostochnyi Matematicheskii Zhurnal, 2011, Volume 11, Number 1, Pages 3–9
(Mi dvmg206)
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This article is cited in 2 scientific papers (total in 2 papers)
Experimental research of Frobenius problem for three arguments
I. S. Vorobjov Pacific National University
Abstract:
The paper describes some numerical results concerning Frobenius problem. Density distribution functions are calculated for $\frac{f(a,b,c)}{\sqrt{abc}}$, $\frac{N(a,b,c)}{\sqrt{abc}}$ and $\frac{N(a,b,c)}{f(a,b,c)}$, where $f(a,b,c)$ is modified Frobenius number (largest integer $M$ such that equation $ax+by+cz=M$ does not have positive integer solution) and $N(a,b,c)$ is modified genus of numerical semigroup generated by $a,b,c$. Expectations of the same ratios are calculated numerically. The paper also contains new sharp lower bound for genus: $N(a,b,c)\geqslant\frac{5\sqrt 3}{9}\sqrt{abc}$.
Key words:
continued fractions, Frobenius numbers.
Received: 29.10.2010
Citation:
I. S. Vorobjov, “Experimental research of Frobenius problem for three arguments”, Dal'nevost. Mat. Zh., 11:1 (2011), 3–9
Linking options:
https://www.mathnet.ru/eng/dvmg206 https://www.mathnet.ru/eng/dvmg/v11/i1/p3
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Abstract page: | 407 | Full-text PDF : | 114 | References: | 79 | First page: | 1 |
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