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

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Authors
Xu, Xi
Issue Date
2018
Type
Thesis
Language
en_US
Keywords
Undergraduate research. , Undergraduate thesis.
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Spine label: Perfect colorings of a design with 2-dimensional euclidean crystallographic.
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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i, 72 leaves: color illustrations.
Includes bibliographical references: leaves 72.
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Wheaton College (MA).
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