Perfect colourings of cyclotomic integers

Perfect colourings of the rings of cyclotomic integers of 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. Thi...

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Main Authors:	Bugarin, Enrico Paolo, De Las Peñas, Ma. Louise Antonette N, Frettlöh, Dirk
Format:	text
Published:	Archīum Ateneo 2013
Subjects:	Colour symmetry Cyclotomic fields Tilings Quasicrystals Mathematics
Online Access:	https://archium.ateneo.edu/mathematics-faculty-pubs/27 https://arxiv.org/abs/0905.4048
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Institution:	Ateneo De Manila University

id	ph-ateneo-arc.mathematics-faculty-pubs-1026
record_format	eprints
spelling	ph-ateneo-arc.mathematics-faculty-pubs-10262021-10-21T05:34:35Z Perfect colourings of cyclotomic integers Bugarin, Enrico Paolo De Las Peñas, Ma. Louise Antonette N Frettlöh, Dirk Perfect colourings of the rings of cyclotomic integers of 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. 2013-01-01T08:00:00Z text application/pdf https://archium.ateneo.edu/mathematics-faculty-pubs/27 https://arxiv.org/abs/0905.4048 Mathematics Faculty Publications Archīum Ateneo Colour symmetry Cyclotomic fields Tilings Quasicrystals Mathematics
institution	Ateneo De Manila University
building	Ateneo De Manila University Library
continent	Asia
country	Philippines Philippines
content_provider	Ateneo De Manila University Library
collection	archium.Ateneo Institutional Repository
topic	Colour symmetry Cyclotomic fields Tilings Quasicrystals Mathematics
spellingShingle	Colour symmetry Cyclotomic fields Tilings Quasicrystals Mathematics Bugarin, Enrico Paolo De Las Peñas, Ma. Louise Antonette N Frettlöh, Dirk Perfect colourings of cyclotomic integers
description	Perfect colourings of the rings of cyclotomic integers of 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.
format	text
author	Bugarin, Enrico Paolo De Las Peñas, Ma. Louise Antonette N Frettlöh, Dirk
author_facet	Bugarin, Enrico Paolo De Las Peñas, Ma. Louise Antonette N Frettlöh, Dirk
author_sort	Bugarin, Enrico Paolo
title	Perfect colourings of cyclotomic integers
title_short	Perfect colourings of cyclotomic integers
title_full	Perfect colourings of cyclotomic integers
title_fullStr	Perfect colourings of cyclotomic integers
title_full_unstemmed	Perfect colourings of cyclotomic integers
title_sort	perfect colourings of cyclotomic integers
publisher	Archīum Ateneo
publishDate	2013
url	https://archium.ateneo.edu/mathematics-faculty-pubs/27 https://arxiv.org/abs/0905.4048
_version_	1715215780547657728

Perfect colourings of cyclotomic integers

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