Similarity Submodules and Root Systems in Four Dimensions

Baake, Michael ; Moody, Robert V.

Canadian journal of mathematics, Tome 51 (1999) no. 6, pp. 1258-1276

Résumé

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.

Détail

DOI : 10.4153/CJM-1999-057-0

Mots-clés : 11S45, 11H05, 52C07

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