Colourings of Cyclotomic Integers with Class Number One

This paper continues the study of colourings of the sets of cyclotomic integers ℳ n = ℤ[ξ n ] (ξ n = e 2πi/n , a primitive nth root of unity) with class number one. We present results for the colour symmetry group and colour preserving group for a given ideal colouring of ℳ n , with φ(n) = 8 and 1...

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Main Authors:	De Las Peñas, Ma. Louise Antonette N, Bugarin, Enrico Paolo, Frettlöh, Dirk
Format:	text
Published:	Archīum Ateneo 2011
Subjects:	colour symmetry ideal colourings Bravais colourings cyclotomic integers non-periodic structures Mathematics
Online Access:	https://archium.ateneo.edu/mathematics-faculty-pubs/101 https://www.tandfonline.com/doi/full/10.1080/14786435.2010.525544?casa_token=1alIuJcN-RkAAAAA%3AlHYMwPGc-9nsmtmCpaiyGthvcSrviHmj_-93u39tr8hsw3lECq3Um5qLC29PmBt26WydUq5LH-thCQ
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Institution:	Ateneo De Manila University

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spelling	ph-ateneo-arc.mathematics-faculty-pubs-11002022-03-18T00:21:14Z Colourings of Cyclotomic Integers with Class Number One De Las Peñas, Ma. Louise Antonette N Bugarin, Enrico Paolo Frettlöh, Dirk This paper continues the study of colourings of the sets of cyclotomic integers ℳ n = ℤ[ξ n ] (ξ n = e 2πi/n , a primitive nth root of unity) with class number one. We present results for the colour symmetry group and colour preserving group for a given ideal colouring of ℳ n , with φ(n) = 8 and 10, thus completing the characterisation of the colour preserving group for the cases φ(n) ≤ 10, where φ is Euler's totient function. 2011-01-01T08:00:00Z text https://archium.ateneo.edu/mathematics-faculty-pubs/101 https://www.tandfonline.com/doi/full/10.1080/14786435.2010.525544?casa_token=1alIuJcN-RkAAAAA%3AlHYMwPGc-9nsmtmCpaiyGthvcSrviHmj_-93u39tr8hsw3lECq3Um5qLC29PmBt26WydUq5LH-thCQ Mathematics Faculty Publications Archīum Ateneo colour symmetry ideal colourings Bravais colourings cyclotomic integers non-periodic structures 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 ideal colourings Bravais colourings cyclotomic integers non-periodic structures Mathematics
spellingShingle	colour symmetry ideal colourings Bravais colourings cyclotomic integers non-periodic structures Mathematics De Las Peñas, Ma. Louise Antonette N Bugarin, Enrico Paolo Frettlöh, Dirk Colourings of Cyclotomic Integers with Class Number One
description	This paper continues the study of colourings of the sets of cyclotomic integers ℳ n = ℤ[ξ n ] (ξ n = e 2πi/n , a primitive nth root of unity) with class number one. We present results for the colour symmetry group and colour preserving group for a given ideal colouring of ℳ n , with φ(n) = 8 and 10, thus completing the characterisation of the colour preserving group for the cases φ(n) ≤ 10, where φ is Euler's totient function.
format	text
author	De Las Peñas, Ma. Louise Antonette N Bugarin, Enrico Paolo Frettlöh, Dirk
author_facet	De Las Peñas, Ma. Louise Antonette N Bugarin, Enrico Paolo Frettlöh, Dirk
author_sort	De Las Peñas, Ma. Louise Antonette N
title	Colourings of Cyclotomic Integers with Class Number One
title_short	Colourings of Cyclotomic Integers with Class Number One
title_full	Colourings of Cyclotomic Integers with Class Number One
title_fullStr	Colourings of Cyclotomic Integers with Class Number One
title_full_unstemmed	Colourings of Cyclotomic Integers with Class Number One
title_sort	colourings of cyclotomic integers with class number one
publisher	Archīum Ateneo
publishDate	2011
url	https://archium.ateneo.edu/mathematics-faculty-pubs/101 https://www.tandfonline.com/doi/full/10.1080/14786435.2010.525544?casa_token=1alIuJcN-RkAAAAA%3AlHYMwPGc-9nsmtmCpaiyGthvcSrviHmj_-93u39tr8hsw3lECq3Um5qLC29PmBt26WydUq5LH-thCQ
_version_	1728621298053021696

Colourings of Cyclotomic Integers with Class Number One

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