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Structure of $Z^2$ modulo selfsimilar sublattices

Roberto Canogar-Mackenzie·Edgar Martinez-Moro
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Abstract

In this paper we show the combinatorial structure of $\mathbb{Z}^2$ modulo sublattices selfsimilar to $\mathbb{Z}^2$. The tool we use for dealing with this purpose is the notion of association scheme. We classify when the scheme defined by the lattice is imprimitive and characterize its decomposition in terms of the decomposition of the gaussian integer defining the lattice. This arise in the classification of different forms of tiling $\mathbb{Z}^2$ by lattices of this type.

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BibTeXRIS

Roberto Canogar-Mackenzie, Edgar Martinez-Moro. 2001-01-10. Structure of $Z^2$ modulo selfsimilar sublattices. https://arxiv.org/abs/math/0101092

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