Czechoslovak Mathematical Journal

, Volume 55, Issue 3, pp 755–772 | Cite as

Numerical Semigroups with a Monotonic Apery Set

  • J. C. Rosales
  • P. A. Garcia-Sanchez
  • J. I. Garcia-Garcia
  • M. B. Branco


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.


numerical semigroups Apery sets symmetric numerical semigroups affine semigroups proportionally modular Diophantine inequality 


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Copyright information

© Mathematical Institute, Academy of Sciences of Czech Republic 2005

Authors and Affiliations

  • J. C. Rosales
    • 1
  • P. A. Garcia-Sanchez
    • 1
  • J. I. Garcia-Garcia
    • 1
  • M. B. Branco
    • 2
  1. 1.Departamento de AlgebraUniversidad de GranadaGranadaSpain
  2. 2.Departamento de MatematicaUniversidade de EvoraEvoraPortugal

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