2008/08/01 by René P. Felix, Rene P. Felix, Manuel Joseph C. Loquias
Engineering · Mathematics · Physics and Astronomy · #Advanced Topology and Set Theory #Color Science and Applications #graph theory and CDMA systems #math.CO #math.GR #msc:05B45 #msc:20B99 #msc:20H15 #msc:52C20
paper · pdf · doi:10.1524/zkri.2008.0053
published as Z. Kristallogr. 223 (2008) 483-491 · 13 pages, 6 figures
openalex publication_date 2008/08/01 · arxiv created 2010/02/02 · arxiv updated 2010/02/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Abstract If G is the symmetry group of an uncolored pattern then a coloring of the pattern is semiperfect if the associated color group H is a subgroup of G of index 2. We give results on how to identify and enumerate all inequivalent semiperfect colorings of certain patterns. This is achieved by treating a coloring as a partition hJ i Y i : i ∈ I, h ∈ H of G , where H is a subgroup of index 2 in G , J i ≤ H for i ∈ I , and Y = ∪ i ∈ I Y i is a complete set of right coset representatives of H in G . We also give a one-to-one correspondence between inequivalent semiperfect colorings whose associated color groups are conjugate subgroups with respect to the normalizer of G in the group of isometries of R n .