Enumerating and identifying semiperfect colorings of symmetrical patterns

Details Enumerating and identifying semiperfect colorings of symmetrical patterns Enumerating and identifying semiperfect colorings of symmetrical patterns

2010-02-02

arxiv.org/abs/1002.0536v1

Z. Kristallogr. 223 (2008) 483-491

Mathematics

Combinatorics

13 pages, 6 figures

Scientific paper

10.1524/zkri.2008.0053

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 $\{hJ_iY_i:i\in I,h\in H\}$ of $G$, where $H$ is a subgroup of index 2 in $G$, $J_i\leq H$ for $i\in I$, and $Y=\cup_{i\in I}{Y_i}$ 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 $\mathbf{R}^n$.

Affiliated with

Also associated with

No associations

Rating

Enumerating and identifying semiperfect colorings of symmetrical patterns does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Enumerating and identifying semiperfect colorings of symmetrical patterns, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Enumerating and identifying semiperfect colorings of symmetrical patterns will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-706955