Similarity submodules and root systems in four dimensions

Details Similarity submodules and root systems in four dimensions Similarity submodules and root systems in four dimensions

1999-04-07

arxiv.org/abs/math/9904028v1

Can. J. Math. 51 (1999) 1258-1276

Mathematics

Metric Geometry

24 pages; written for a special issue of Can. J. Math. in honour of H.S.M. Coxeter

Scientific paper

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.

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