Constructing the set of complete intersection numerical semigroups with a given Frobenius number

1. Bertin, J., Carbonne, P.: Semi-groupes d’entiers et application aux branches. J. Algebra 49, 81–95 (1977)

   Article  MathSciNet  MATH  Google Scholar 

2. Bermejo, I., García-Marco, I., Salazar-González, J.J.: An algorithm for checking whether the toric ideal of an affine monomial curve is a complete intersection. J. Symb. Comput. 42, 971–991 (2007)

   Article  MATH  Google Scholar 

3. Bermejo, I., Gimenez, P., Reyes, E., Villarreal, R.H.: Complete intersections in affine monomial curves. Bol. Soc. Mat. Mexicana (3) 11(2), 191–203 (2005)

   Google Scholar 

4. Bras-Amorós, M.: Fibonacci-like behavior of the number of numerical semigroups of a given genus. Semigroup Forum 76, 379–384 (2008)

   Article  MathSciNet  MATH  Google Scholar 

5. Delorme, C.: Sous-monoïdes d’intersection complète de \({\mathbb{N}}\). Ann. Scient. École Norm. Sup. 4(9), 145–154 (1976)

   MathSciNet  Google Scholar 

6. Delgado, M.: Experiments with numerical semigroups (in preparation)

7. Delgado, M., García-Sánchez, P.A., Morais, J.: “Numericalsgps”: a gap package on numerical semigroups. (http://www.gap-system.org/Packages/numericalsgps.html)

8. The GAP Group, GAP—Groups, algorithms, and programming, version 4.4; 2004. (http://www.gap-system.org)

9. García-Sánchez, P.A., Ojeda, I., Rosales, J.C.: Affine semigroups having a unique Betti element. J. Algebra Appl. 12 1250177 (11 pages) (2013)

10. Herzog, J., Kunz, E.: Die Wertehalbgruppe eines lokalen Rings der Dimension 1, S. B. Heidelberger Akad. Wiss. Math. Natur. Kl 2767 (1971)

11. Johnson, S.M.: A linear Diophantine problem. Can. J. Math. 12, 390–398 (1960)

    Article  MATH  Google Scholar 

12. Kirfel, C., Pellikaan, R.: The minimum distance of codes in an array coming from telescopic semigroups. IEEE Trans. Inform. Theory 41, 1720–1732 (1995). Special issue on algebraic geometry codes

    Article  MathSciNet  MATH  Google Scholar 

13. Ramírez Alfonsín, J.L.: The Diophantine Frobenius Problem, Oxford Lectures Series in Mathematics and its Applications, vol. 30. Oxford University Press (2005)

14. Rosales, J.C.: On presentations of subsemigroups of \({\mathbb{N}}^{n}\). Semigroup Forum 55, 152–159 (1997)

    Article  MathSciNet  MATH  Google Scholar 

15. Rosales, J.C., García-Sánchez, P.A.: On numerical semigroups with high embedding dimension. J. Algebra 203, 567–578 (1998)

    Google Scholar 

16. Rosales, J.C., García-Sánchez, P.A.: On free affine semigroups. Semigroup Forum 58(3), 367–385 (1999)

    MathSciNet  MATH  Google Scholar 

17. Rosales, J.C., García-Sánchez, P.A.: Numerical Semigroups, Developments in Mathematics, vol. 20. Springer, New York (2009)

    Book  Google Scholar 

18. Rosales, J.C., García-Sánchez, P.A., García-García, J.I., Jiménez-Madrid, J.A.: Fundamental gaps in numerical semigroups. J. Pure Appl. Alg. 189, 301–313 (2004)

    Article  MATH  Google Scholar 

19. Zhai, A.: Fibonacci-like growth of numerical semigroups of a given genus, arXiv:1111.3142

20. Zariski, O.: Le problème des modules pour les courbes planes. Hermann (1986)

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