Abstract
Letg be a positive integer. We prove that there are positive integersn 1,n 2,n 3 andn 4 such that the semigroupS=(n 1,n 2,n 3,n 4) is an irreducible (symmetric or pseudosymmetric) numerical semigroup with g(S)=g.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Apéry, R., Sur les branches superlinéaires des courbes algébriques,C. R. Acad. Sci. Paris 222 (1946), 1198–1200.
Barucci, V., Dobbs, D. E. andFontana, M.,Maximality Properties in Numerical Semigroups and Applications to One-Dimensional Analytically Irreducible Local Domains, Mem. Amer. Math. Soc.125, Amer. Math. Soc., Providence, R. I., 1997.
Curtis, F., On formulas for the Frobenius number of a numerical semigroup,Math. Scand. 67 (1990), 190–192.
Fröberg, R., Gottlieb, C. andHäggkvist, R., On numerical semigroups,Semigroup Forum 35 (1987), 63–83.
Ramírez Alfonsín, J. L., The Diophantine Frobenius problemPreprint, Forschungsinstitut für Diskrete Mathematik, Bonn, 2000.
Rosales, J. C. andBranco, M. B., Numerical semigroups that can be expressed as an intersection of symmetric numerical semigroups,J. Pure Appl. Algebra 171 (2002), 303–314.
Rosales, J. C. andBranco, M. B., Decomposition of a numerical semigroup as an intersection of irreducible numerical semigroups,Bull. Belg. Math. Soc. 9 (2002), 373–381.
Rosales, J. C. andBranco, M. B., Irreducible numerical semigroups,Pacific J. Math. 209 (2003), 131–143.
Rosales, J. C., García-Sánchez, P. A. andGarcía-García, J. I., Every positive integer is the Frobenius number of a numerical semigroup with three generators,Preprint, 2003.
Rosales, J. C., García-Sánchez, P. A., García-García, J. I. andJiménez-Madrid, J. A., The oversemigroups of a numerical semigroup,Semigroup Forum 67 (2003), 145–158.
Sylvester, J. J., Mathematical questions with their solutions,Educational Times 41 (1884), 21.
Author information
Authors and Affiliations
Additional information
This work has been supported by the project BFM2000-1469.
Rights and permissions
About this article
Cite this article
García-Sánchez, P.A., Rosales, J.C. Every positive integer is the Frobenius number of an irreducible numerical semigroup with at most four generators. Ark. Mat. 42, 301–306 (2004). https://doi.org/10.1007/BF02385481
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02385481