Similarity submodules and root systems in four dimensions
arXiv:math/9904028
Abstract
Lattices and Z-modules in Euclidean space possess an infinitude of subsets that are images of the original set under similarity transformation. We classify such self-similar images according to their indices for certain 4D examples that are related to 4D root systems, both crystallographic and non-crystallographic. We encapsulate their statistics in terms of Dirichlet series generating functions and derive some of their asymptotic properties.
24 pages; written for a special issue of Can. J. Math. in honour of H.S.M. Coxeter