Numerical semigroups with a monotonic Apéry set

José Carlos Rosales; Pedro A. García-Sánchez; Juan Ignacio García-García; M. B. Branco

Czechoslovak Mathematical Journal (2005)

  • Volume: 55, Issue: 3, page 755-772
  • ISSN: 0011-4642

Abstract

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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 < w ( 1 ) < ⋯ < w ( m - 1 ) . 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.

How to cite

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Rosales, José Carlos, et al. "Numerical semigroups with a monotonic Apéry set." Czechoslovak Mathematical Journal 55.3 (2005): 755-772. <http://eudml.org/doc/30985>.

@article{Rosales2005,
abstract = {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 $0<w(1)<\dots <w(m-1)$. 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.},
author = {Rosales, José Carlos, García-Sánchez, Pedro A., García-García, Juan Ignacio, Branco, M. B.},
journal = {Czechoslovak Mathematical Journal},
keywords = {numerical; semigroups; Apéry; sets; symmetric; affine; proportionally; modular; Diophantine; inequality; numerical semigroups; Apéry sets; affine semigroups; modular Diophantine inequalities; multiplicities; embedding dimensions; Frobenius numbers},
language = {eng},
number = {3},
pages = {755-772},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Numerical semigroups with a monotonic Apéry set},
url = {http://eudml.org/doc/30985},
volume = {55},
year = {2005},
}

TY - JOUR
AU - Rosales, José Carlos
AU - García-Sánchez, Pedro A.
AU - García-García, Juan Ignacio
AU - Branco, M. B.
TI - Numerical semigroups with a monotonic Apéry set
JO - Czechoslovak Mathematical Journal
PY - 2005
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 55
IS - 3
SP - 755
EP - 772
AB - 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 $0<w(1)<\dots <w(m-1)$. 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.
LA - eng
KW - numerical; semigroups; Apéry; sets; symmetric; affine; proportionally; modular; Diophantine; inequality; numerical semigroups; Apéry sets; affine semigroups; modular Diophantine inequalities; multiplicities; embedding dimensions; Frobenius numbers
UR - http://eudml.org/doc/30985
ER -

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