FAR EASTERN BRANCH OF THE RUSSIAN ACADEMY OF SCIENCES
INSTITUTE OF APPLIED MATHEMATICS KHABAROVSK DIVISION
Far Eastern Mathematical Journal
Experimental research of Frobenius problem for three arguments |
I. S. Vorobjov |
2011, issue 1, P. 3–9 |
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: $N(a,b,c) \ge \frac{5\sqrt{3}}{9}\sqrt{abc}$. |
Keywords: continued fractions, Frobenius numbers |
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References |
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