1. CJM 1999 (vol 51 pp. 1258)
|Similarity Submodules and Root Systems in Four Dimensions |
Lattices and $\ZZ$-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.
Categories:11S45, 11H05, 52C07