Equivalence of primitive sets
Prikladnaya Diskretnaya Matematika. Supplement, no. 6 (2013), pp. 20-24.

Voir la notice de l'article provenant de la source Math-Net.Ru

Equivalence of primitive sets of natural numbers is investigated in connection with the diophantine Frobenius problem. The equivalence is used to simplify calculations of Frobenius number $g(a_1,\ldots,a_k)$ and all numbers that are not contained in the additive semigroup generated by the set $\{a_1,\ldots,a_k\}$.
Keywords: Frobenius's function, primitive set, additive semigroups of numbers.
@article{PDMA_2013_6_a10,
     author = {V. M. Fomichev},
     title = {Equivalence of primitive sets},
     journal = {Prikladnaya Diskretnaya Matematika. Supplement},
     pages = {20--24},
     publisher = {mathdoc},
     number = {6},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDMA_2013_6_a10/}
}
TY  - JOUR
AU  - V. M. Fomichev
TI  - Equivalence of primitive sets
JO  - Prikladnaya Diskretnaya Matematika. Supplement
PY  - 2013
SP  - 20
EP  - 24
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PDMA_2013_6_a10/
LA  - ru
ID  - PDMA_2013_6_a10
ER  - 
%0 Journal Article
%A V. M. Fomichev
%T Equivalence of primitive sets
%J Prikladnaya Diskretnaya Matematika. Supplement
%D 2013
%P 20-24
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PDMA_2013_6_a10/
%G ru
%F PDMA_2013_6_a10
V. M. Fomichev. Equivalence of primitive sets. Prikladnaya Diskretnaya Matematika. Supplement, no. 6 (2013), pp. 20-24. http://geodesic.mathdoc.fr/item/PDMA_2013_6_a10/

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

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

[3] Fomichev V. M., “Reshenie diofantovoi problemy Frobeniusa”, Diskretnaya matematika, 2013, no. 2

[4] Curtis F., “On formulas for the Frobenius number of a numerical semigroup”, Math. Scand., 67 (1990), 190–192 | 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., 1964, no. 6, 346–354 | DOI | MR | Zbl

[6] Heap B. R., Lynn M. S., “On a linear diophantine problem of Frobenius: an improved algorithm”, Numerische Math., 1965, no. 7, 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””, The American Mathematical 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