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Affine convex body semigroups

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Abstract

In this paper we present a new class of semigroups called convex body semigroups which are generated by convex bodies of ℝk. They generalize to arbitrary dimension the concept of proportionally modular numerical semigroups of Rosales et al. (J. Number Theory 103, 281–294, 2003). Several properties of these semigroups are proven. Affine convex body semigroups obtained from circles and polygons of ℝ2 are characterized. The algorithms for computing minimal system of generators of these semigroups are given. We provide the implementation of some of them.

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Notes

  1. For the initial values of i it is possible to obtain that C i ∩C i+1=∅, see Fig. 5.

  2. Note the point T 1 is a natural multiple of the point τ 2∩C and that T 2=2T 1.

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Authors and Affiliations

  1. Departamento de Matemáticas, Universidad de Cádiz, 11510, Puerto Real, Cádiz, Spain

    J. I. García-García & M. A. Moreno-Frías

  2. Universidad de Cádiz, Departamento Lenguajes y Sistemas Informáticos, 11405, Jerez de la Frontera, Cádiz, Spain

    A. Sánchez-R.-Navarro & A. Vigneron-Tenorio

Authors
  1. J. I. García-García
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  2. M. A. Moreno-Frías
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  3. A. Sánchez-R.-Navarro
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  4. A. Vigneron-Tenorio
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Corresponding author

Correspondence to J. I. García-García.

Additional information

Communicated by Fernando Torres.

J.I. García-García partially supported by MTM2007-62346 and Junta de Andalucía group FQM-366. M.A. Moreno-Frías partially supported by MTM2008-06201-C02-02 and Junta de Andalucía group FQM-298. A. Sánchez-R.-Navarro partially supported by Junta de Andalucía group FQM-366. A. Vigneron-Tenorio partially supported by MTM2007-64704 and Junta de Andalucía group FQM-366.

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García-García, J.I., Moreno-Frías, M.A., Sánchez-R.-Navarro, A. et al. Affine convex body semigroups. Semigroup Forum 87, 331–350 (2013). https://doi.org/10.1007/s00233-012-9460-9

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  • DOI: https://doi.org/10.1007/s00233-012-9460-9

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