Geodesic
Numerical semigroups with a monotonic Apéry set
Czechoslovak Mathematical Journal, Tome 55 (2005) no. 3, pp. 755-772

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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 
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     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},
     publisher = {mathdoc},
     volume = {55},
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     zbl = {1081.20071},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2005__55_3_a16/}
}
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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/