Affine convex body semigroups
  In this paper we present a new kind of semigroups called convex body semigroups which are generated by convex bodies of R^k. 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 R^2 are characterized. The algorithms for computing minimal system of generators of these semigroups are given. We provide the implementation of some of them. 
J. I. Garc\'ia-Garc\'ia, M. A. Moreno-Fr\'ias, A.   S\'anchez-R.-Navarro, A. Vigneron-Tenorio
math.AC