Counting perfect colourings of plane regular tilings

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dc.creatorFrettlöh, Dirk
dc.date2008-07-29
dc.date.accessioned2026-07-07T09:53:29Z
dc.date.available2026-07-07T09:53:29Z
dc.descriptionA first step in investigating colour symmetries of periodic and nonperiodic patterns is determining the number of colours which allow perfect colourings of the pattern under consideration. A perfect colouring is one where each symmetry of the uncoloured pattern induces a global permutation of the colours. Two cases are distinguished: Either perfect colourings with respect to all symmetries, or with respect to orientation preserving symmetries only (no reflections). For the important class of colourings of regular tilings (and some Laves tilings) of the Euclidean or hyperbolic plane, this mainly combinatorial question is addressed here using group theoretical methods.
dc.description6 pages, 1 figure, accepted for Z. Krist
dc.identifierhttps://arxiv.org/abs/0807.4630
dc.identifierhttp://arxiv.org/abs/0807.4630
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/165973
dc.subjectCombinatorics
dc.subjectGroup Theory
dc.subject05A15
dc.titleCounting perfect colourings of plane regular tilings
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