Perfect colourings of cyclotomic integers
Group Theory
2012-02-22 v2 Combinatorics
Abstract
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.
Cite
@article{arxiv.0905.4048,
title = {Perfect colourings of cyclotomic integers},
author = {E. P. Bugarin and M. L. A. N. de las Peñas and D. Frettlöh},
journal= {arXiv preprint arXiv:0905.4048},
year = {2012}
}
Comments
11 pages, 1 bw figure, 1 colour figure