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Similarity Submodules and Root Systems in Four Dimensions

Published online by Cambridge University Press:  20 November 2018

Michael Baake  and
Robert V. Moody
Michael Baake
Affiliation:
Institut für Theoretische Physik, Universität Tübingen, Auf der Morgenstelle 14, D-72076 Tübingen, Germany
Robert V. Moody
Affiliation:
Department of Mathematical Sciences, University of Alberta, Edmonton, Alberta, T6G 2G1
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Abstract

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Lattices and $\mathbb{Z}$-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.

Keywords

11S4511H0552C07
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 51 , Issue 6 , 01 December 1999 , pp. 1258 - 1276
Copyright
Copyright © Canadian Mathematical Society 1999

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