# Invariant Submodules and Semigroups of Self-Similarities for Fibonacci Modules

@article{Baake1998InvariantSA, title={Invariant Submodules and Semigroups of Self-Similarities for Fibonacci Modules}, author={Michael Baake and Robert V. Moody}, journal={arXiv: Mathematical Physics}, year={1998} }

The problem of invariance and self-similarity in Z-modules is investigated. For a selection of examples relevant to quasicrystals, especially Fibonacci modules, we determine the semigroup of self-similarities and encapsulate the number of similarity submodules in terms of Dirichlet series generating functions.

## 3 Citations

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The similarity submodules for various lattices and modules of interest in the crystal and quasicrystal theory are determined and the corresponding semigroups, along with their zeta functions, are…

### Similarity Submodules and Root Systems in Four Dimensions

- MathematicsCanadian Journal of Mathematics
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Abstract 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…

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