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    Perfect colorings of a design with 2-dimensional euclidean crystallographic symmetry group.

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    Abstract_Fiona_Xi_Xu.pdf (42.89Kb)
    Certification by Registrar_Fiona_Xi_Xu.pdf (31.75Kb)
    Thesis_Fiona_Xi_Xu.pdf (953.0Kb)
    Date
    2018
    Author
    Xu, Xi
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    Abstract
    This thesis introduces perfect colorings and the systematic way of generating perfect colorings. We study the perfect colorings for designs whose symmetry groups are 2-dimensional Euclidean crystallographic groups. Two-dimensional Euclidean crys- tallographic groups are discrete subgroups of the isometry group of the Euclidean plane. We classify crystallographic groups by their ranks. Crystallographic groups of rank 0, rank 1, and rank 2 are explained with details and examples. Theorems that related to the number of perfect colorings for designs with crystallographic symmetry groups are constructed and proved.
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    http://hdl.handle.net/11040/24564
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    • Mathematics [8]
    • File:Abstract_Fiona_Xi_Xu.pdf
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      File Size:42.89Kb
    • File:Certification by Registrar_Fiona_Xi_Xu.pdf
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      File Size:31.75Kb
    • File:Thesis_Fiona_Xi_Xu.pdf
      MIME type:application/pdf
      File Size:953.0Kb

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