Affine convex body semigroups
Abstract
In this paper we present a new kind 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 semigroup of [7]. 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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