Perfect colourings of cyclotomic integers

Details Perfect colourings of cyclotomic integers Perfect colourings of cyclotomic integers

2009-05-25

arxiv.org/abs/0905.4048v2

Mathematics

Group Theory

11 pages, 1 bw figure, 1 colour figure

Scientific paper

Perfect colourings of the rings of cyclotomic integers with class number one are studied. It is shown that all colourings induced by ideals (q) are chirally perfect, and vice versa. A necessary and sufficient condition for a colouring to be perfect is obtained, depending on the factorisation of q. This result yields the colour symmetry group H in general. Furthermore, the colour preserving group K is determined in all but finitely many cases. An application to colourings of quasicrystals is given.

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