On Bravais colourings of cyclotomic integers with class number one

Abstract

Given a Bravais colouring of planar modules $\M_n:=\Z[ξ_n]$, where ${\xi }_n$ 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.

9 pages, 2 tables

References in corpus (1)

• Bravais colourings of planar modules with N-fold symmetry