2008/07/29 by Dirk Frettlöh, Frettlöh, Dirk
Engineering · Mathematics · #05A15 #Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR) #graph theory and CDMA systems #math.CO #math.GR #msc:05A15
paper · pdf · doi:10.48550/arxiv.0807.4630
6 pages, 1 figure, accepted for Z. Krist
arxiv created 2008/07/29 · openalex publication_date 2008/07/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
A 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.