Colourings of Cyclotomic Integers with Class Number One

Authors

Ma. Louise Antonette N. De Las Peñas, Ateneo de Manila UniversityFollow
Enrico Paolo Bugarin
Dirk Frettlöh, Universitat Bielefeld

Document Type

Article

Publication Date

2011

Abstract

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.

Recommended Citation

Ma. Louise Antonette N. de Las Peñas, Enrico Paolo Bugarin & Dirk Frettlöh (2011) Colourings of cyclotomic integers with class number one, Philosophical Magazine, 91:19-21, 2690-2699, DOI: 10.1080/14786435.2010.525544