Work

Affine Semigroups Without Consecutive Small Elements

Year: 2026

Type: article

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

Source: Journal of Mathematics

DOI: 10.1155/jom/9042510

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

Institutions: Universidad de Granada, Universidad de Cádiz

Language: English

Topic: Commutative Algebra and Its Applications

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,160

Funder: Universidad de Cádiz