Geodesic
Numerical semigroups with a monotonic Apéry set
Czechoslovak Mathematical Journal, Tome 55 (2005) no. 3, pp. 755-772
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

We study numerical semigroups $S$ with the property that if $m$ is the multiplicity of $S$ and $w(i)$ is the least element of $S$ congruent with $i$ modulo $m$, then $0
We study numerical semigroups $S$ with the property that if $m$ is the multiplicity of $S$ and $w(i)$ is the least element of $S$ congruent with $i$ modulo $m$, then $0$. The set of numerical semigroups with this property and fixed multiplicity is bijective with an affine semigroup and consequently it can be described by a finite set of parameters. Invariants like the gender, type, embedding dimension and Frobenius number are computed for several families of this kind of numerical semigroups.
Classification : 11D75, 13H10, 20M14
Keywords: numerical; semigroups; Apéry; sets; symmetric; affine; proportionally; modular; Diophantine; inequality 
@article{CMJ_2005_55_3_a16,
     author = {Rosales, J. C. and Garc{\'\i}a-S\'anchez, P. A. and Garc{\'\i}a-Garc{\'\i}a, J. I. and Branco, M. B.},
     title = {Numerical semigroups with a monotonic {Ap\'ery} set},
     journal = {Czechoslovak Mathematical Journal},
     pages = {755--772},
     year = {2005},
     volume = {55},
     number = {3},
     mrnumber = {2153099},
     zbl = {1081.20071},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2005_55_3_a16/}
}
TY  - JOUR
AU  - Rosales, J. C.
AU  - García-Sánchez, P. A.
AU  - García-García, J. I.
AU  - Branco, M. B.
TI  - Numerical semigroups with a monotonic Apéry set
JO  - Czechoslovak Mathematical Journal
PY  - 2005
SP  - 755
EP  - 772
VL  - 55
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/CMJ_2005_55_3_a16/
LA  - en
ID  - CMJ_2005_55_3_a16
ER  - 
%0 Journal Article
%A Rosales, J. C.
%A García-Sánchez, P. A.
%A García-García, J. I.
%A Branco, M. B.
%T Numerical semigroups with a monotonic Apéry set
%J Czechoslovak Mathematical Journal
%D 2005
%P 755-772
%V 55
%N 3
%U http://geodesic.mathdoc.fr/item/CMJ_2005_55_3_a16/
%G en
%F CMJ_2005_55_3_a16
Rosales, J. C.; García-Sánchez, P. A.; García-García, J. I.; Branco, M. B. Numerical semigroups with a monotonic Apéry set. Czechoslovak Mathematical Journal, Tome 55 (2005) no. 3, pp. 755-772. http://geodesic.mathdoc.fr/item/CMJ_2005_55_3_a16/

[1] F.  Ajili and E.  Contejean: Avoiding slack variables in the solving of linear Diophantine equations and inequations. Principles and practice of constraint programming. Theoret. Comput. Sci. 173 (1997), 183–208. | DOI | MR

[2] R.  Apéry: Sur les branches superlinéaires des courbes algébriques. C. R. Acad. Sci. Paris 222 (1946). | MR

[3] V.  Barucci, D. E.  Dobbs and M.  Fontana: Maximality Properties in Numerical Semigroups and Applications to One-Dimensional Analytically Irreducible Local Domains. Memoirs of the Amer. Math. Soc. Vol. 598. , 1997. | MR

[4] J.  Bertin and P.  Carbonne: Semi-groupes d’entiers et application aux branches. J.  Algebra 49 (1987), 81–95. | DOI | MR

[5] A.  Brauer: On a problem of partitions. Amer. J.  Math. 64 (1942), 299–312. | DOI | MR | Zbl

[6] H.  Bresinsky: On prime ideals with generic zero $x_i=t^{n_i}$. Proc. Amer. Math. Soc. 47 (1975), 329–332. | MR

[7] E.  Contejean and H.  Devie: An efficient incremental algorithm for solving systems of linear diophantine equations. Inform. and Comput. 113 (1994), 143–172. | DOI | MR

[8] C.  Delorme: Sous-monoïdes d’intersection complète de  $\mathbb{N}$. Ann. Scient. École Norm. Sup. 9 (1976), 145–154. | DOI | MR

[9] R.  Fröberg, C.  Gottlieb and R.  Häggkvist: Semigroups, semigroup rings and analytically irreducible rings. Reports Dpt. of Mathematics, University of Stockholm, Vol.  1, 1986.

[10] R.  Fröberg, C.  Gottlieb and R.  Häggkvist: On numerical semigroups. Semigroup Forum 35 (1987), 63–83. | DOI

[11] P. A.  García-Sánchez and J. C.  Rosales: Numerical semigroups generated by intervals. Pacific J.  Math. 191 (1999), 75–83. | DOI

[12] R.  Gilmer: Commutative Semigroup Rings. The University of Chicago Press, 1984. | MR | Zbl

[13] J.  Herzog: Generators and relations of abelian semigroups and semigroup rings. Manuscripta Math 3 (1970), 175–193. | DOI | MR | Zbl

[14] E.  Kunz: The value-semigroup of a one-dimensional Gorenstein ring. Proc. Amer. Math. Soc. 25 (1973), 748–751. | DOI | MR

[15] J. L.  Ramírez Alfonsín: The Diophantine Frobenius problem. Forschungsintitut für Diskrete Mathematik, Bonn, Report No.00893, 2000.

[16] J. L.  Ramírez Alfonsín: The Diophantine Frobenius problem, manuscript.

[17] J. C.  Rosales: On numerical semigroups. Semigroup Forum 52 (1996), 307–318. | DOI | MR | Zbl

[18] J. C.  Rosales: On symmetric numerical semigroups. J.  Algebra 182 (1996), 422–434. | DOI | MR | Zbl

[19] J. C.  Rosales and M. B.  Branco: Numerical semigroups that can be expressed as an intersection of symmetric numerical semigroups. J. Pure Appl. Algebra 171 (2002), 303–314. | DOI | MR

[20] J. C.  Rosales and P. A.  García-Sánchez: Finitely Generated Commutative Monoids. Nova Science Publishers, New York, 1999. | MR

[21] J. C.  Rosales, P. A.  García-Sánchez, J. I.  García-García and M. B.  Branco: Systems of inequalities and numerical semigroups. J.  London Math. Soc. 65 (2002), 611–623. | DOI | MR

[22] J. C.  Rosales, P. A. García-Sánchez, J. I.  García-García and J. M. Urbano-Blanco: Proportionally modular Diophantine inequalities. J.  Number Theory 103 (2003), 281–294. | DOI | MR

[23] E. S.  Selmer: On a linear Diophantine problem of Frobenius. J.  Reine Angew. Math. 293/294 (1977), 1–17. | MR

[24] K.  Watanabe: Some examples of one dimensional Gorenstein domains. Nagoya Math.  J. 49 (1973), 101–109. | DOI | MR | Zbl