Geodesic growth in virtually abelian groups
arXiv:1908.07294 · doi:10.1016/j.jalgebra.2020.12.003
Abstract
We show that the geodesic growth function of any finitely generated virtually abelian group is either polynomial or exponential; and that the geodesic growth series is holonomic, and rational in the polynomial growth case. In addition, we show that the language of geodesics is blind multicounter.
23 pages, 1 figure, improved readability