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- Q7092304 subject Q7214710.
- Q7092304 subject Q7217286.
- Q7092304 subject Q8485348.
- Q7092304 subject Q8800321.
- Q7092304 abstract "A one-dimensional symmetry group is a mathematical group that describes symmetries in one dimension (1D). A pattern in 1D can be represented as a function f(x) for, say, the color at position x.The only nontrivial point group in 1D is a simple reflection. It can be represented by the simplest Coxeter group, A1, [ ], or Coxeter-Dynkin diagram File:CDel node.png.Affine symmetry groups represent translation. Isometries which leave the function unchanged are translations x + a with a such that f(x + a) = f(x) and reflections a − x with a such that f(a − x) = f(x). The reflections can be represented by the affine Coxeter group [∞], or Coxeter-Dynkin diagram File:CDel node.pngFile:CDel infin.pngFile:CDel node.png representing two reflections, and the translational symmetry as [∞]+, or Coxeter-Dynkin diagram File:CDel node h2.pngFile:CDel infin.pngFile:CDel node h2.png as the composite of two reflections.".
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- Q7092304 comment "A one-dimensional symmetry group is a mathematical group that describes symmetries in one dimension (1D). A pattern in 1D can be represented as a function f(x) for, say, the color at position x.The only nontrivial point group in 1D is a simple reflection. It can be represented by the simplest Coxeter group, A1, [ ], or Coxeter-Dynkin diagram File:CDel node.png.Affine symmetry groups represent translation.".
- Q7092304 label "One-dimensional symmetry group".