Geodesic
Experimental research of Frobenius problem for three arguments
Dalʹnevostočnyj matematičeskij žurnal, Tome 11 (2011) no. 1, pp. 3-9

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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: $N(a,b,c)\geqslant\frac{5\sqrt 3}{9}\sqrt{abc}$. 
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     author = {I. S. Vorobjov},
     title = {Experimental research of {Frobenius} problem for three arguments},
     journal = {Dalʹnevosto\v{c}nyj matemati\v{c}eskij \v{z}urnal},
     pages = {3--9},
     publisher = {mathdoc},
     volume = {11},
     number = {1},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DVMG_2011_11_1_a0/}
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I. S. Vorobjov. Experimental research of Frobenius problem for three arguments. Dalʹnevostočnyj matematičeskij žurnal, Tome 11 (2011) no. 1, pp. 3-9. http://geodesic.mathdoc.fr/item/DVMG_2011_11_1_a0/