Affine convex body semigroups

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.