Geodesic
Primitive sets of numbers being equivalent by Frobenius
Prikladnaâ diskretnaâ matematika, no. 1 (2014), pp. 20-26 Cet article a éte moissonné depuis la source Math-Net.Ru

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Equivalence of primitive sets of natural numbers is investigated in connection with the Diophantine Frobenius problem. The equivalence is used for simplifying calculations of Frobenius number $g(a_1,\dots,a_k)$ and of the whole set of numbers that are not contained in the additive semigroup generated by a set $\{a_1,\dots,a_k\}$.
Keywords: Frobenius number, primitive set, additive semigroup generated by set of numbers. 
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V. M. Fomichev. Primitive sets of numbers being equivalent by Frobenius. Prikladnaâ diskretnaâ matematika, no. 1 (2014), pp. 20-26. http://geodesic.mathdoc.fr/item/PDM_2014_1_a2/

[1] Sylvester J. J., “Problem 7382”, Mathematical Questions from the Educational Times, 37 (1884), 26

[2] Curtis F., “On formulas for the Frobenius number of a numerical semigroup”, Math. Scand., 67 (1990), 190–192 | MR | Zbl

[3] Fomichev V. M., “Ekvivalentnost primitivnykh mnozhestv”, Prikladnaya diskretnaya matematika. Prilozhenie, 2013, no. 6, 20–24

[4] Alfonsin J. R., The Diophantine Frobenius Problem, Oxford University Press, 2005 | MR | Zbl

[5] Heap B. R., Lynn M. S., “A graph-theoretic algorithm for the solution of a linear Diophantine problem of Frobenius”, Numerische Math., 6 (1964), 346–354 | DOI | MR | Zbl

[6] Heap B. R., Lynn M. S., “On a linear Diophantine problem of Frobenius: an improved algorithm”, Numerische Math., 7 (1965), 226–231 | DOI | MR | Zbl

[7] Bogart C., Calculating Frobenius numbers with Boolean Toeplitz matrix multiplication, For Dr. Cull, CS 523, Oregon State University, March 17, 2009

[8] Nijenhuis M., “A minimal-path algorithm for the ‘money changing problem’ ”, Am. Math. Monthly, 86 (1979), 832–835 | DOI | MR | Zbl

[9] Bocker S., Liptak Z., The “money changing problem” revisited: computing the Frobenius number in time O$(ka_1)$, Technical Report No. 2004-2, Univ. of Bielefeld, Technical Faculty, 2004 | MR