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arXiv · 1207.2322

On Bravais colourings of cyclotomic integers with class number one

Enrico Paolo Bugarin
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Abstract

Given a Bravais colouring of planar modules $\M_n:=\Z[ξ_n]$, where $ξ_n$ is a primitive $n$th root of unity, two important colour groups arise: the colour symmetry group $H$, which permutes the colours of a given colouring of $\M_n$, and the colour preserving group $K$, a normal subgroup of $H$ that fixes the colours. This paper gives a complete characterisation of $H$ and $K$ for all $\ell$-colourings of $\M_n$ for values of $n$ for which $\M_n$ has class number one.

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Enrico Paolo Bugarin. 2012-07-10. On Bravais colourings of cyclotomic integers with class number one. https://arxiv.org/abs/1207.2322

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