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Affine Semigroups Without Consecutive Small Elements

Author

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  • J. C. Rosales
  • R. Tapia-Ramos
  • A. Vigneron-Tenorio

Abstract

An A-semigroup is a numerical semigroup without consecutive small elements. This work generalizes this concept to finite-complement submonoids of an affine cone C. We develop algorithmic procedures to compute all A-semigroups with a given Frobenius element (denoted by Af) and with fixed Frobenius element and multiplicity. Moreover, we analyze the Af-systems of generators. Furthermore, we study A-numerical semigroups with maximal embedding dimension, a fixed Frobenius number. and multiplicity, providing an algorithm for their computation and a graphical classification.

Suggested Citation

  • J. C. Rosales & R. Tapia-Ramos & A. Vigneron-Tenorio, 2026. "Affine Semigroups Without Consecutive Small Elements," Journal of Mathematics, Hindawi, vol. 2026, pages 1-14, October.
    • Handle: RePEc:hin:jjmath:9042510
    DOI: 10.1155/jom/9042510
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