Affine Semigroups Without Consecutive Small Elements

J. C. Rosales, R. Tapia-Ramos and A. Vigneron-Tenorio

Journal of Mathematics, 2026, vol. 2026, 1-14

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.

Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:9042510

DOI: 10.1155/jom/9042510

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