Combinator ial Designs - Columbia Universitycs4205/files/CM10.pdf · Chapter 10 Combinator ial...
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Chapter 10 Combinatorial Designs 10.1 Latin Squares 10.2 Block Designs 10.3 Classical Finite Geometries 10.4 Projective Planes 10.5 Affine Planes 1
Transcript of Combinator ial Designs - Columbia Universitycs4205/files/CM10.pdf · Chapter 10 Combinator ial...
Chapter 10Combinatorial Designs10.1 Latin Squares10.2 Block Designs10.3 Classical Finite Geometries10.4 Projective Planes10.5 Affine Planes
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10.1 LATIN SQUARES
Fig 10.1.1
Section 10.1 Latin Squares 3
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Product of Latin Squares
Section 10.1 Latin Squares 5
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Orthogonal Latin Squares
Section 10.1 Latin Squares 7
Fig 10.1.2
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Section 10.1 Latin Squares 9
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Section 10.1 Latin Squares 11
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Isotopic Latin Squares
Section 10.1 Latin Squares 13
Abstract Latin Squares
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Section 10.1 Latin Squares 15
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Section 10.2 Block Designs 17
10.2 BLOCK DESIGNS
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Balanced Designs
Section 10.2 Block Designs 19
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Necessary Conditions
Section 10.2 Block Designs 21
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Section 10.2 Block Designs 23
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Steiner Triple Systems
Section 10.2 Block Designs 25
Constructing Designs
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Section 10.2 Block Designs 27
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Section 10.2 Block Designs 29
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Isomorphism of Designs
Section 10.2 Block Designs 31
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10.3 CLASSICAL FINITE GEOMETRY
Section 10.3 Classical Finite Geometry 33
Fig 10.3.1
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Fig 10.3.2
The Fano Plane
Section 10.3 Classical Finite Geometry 35
Fig 10.3.3
The Pappus Geometry
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Fig 10.3.4
Section 10.3 Classical Finite Geometry 37
The Desargues Geometry
Fig 10.3.5
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Section 10.3 Classical Finite Geometry 39
Partially Balanced Designs
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10.4 PROJECTIVE PLANES
Some Basic Examples
Section 10.4 Projective Planes 41
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Section 10.4 Projective Planes 43
Duality Principle for Projective Planes
Fig 10.4.1
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Projective Planes as BIBD’s
Fig 10.4.2
Section 10.4 Projective Planes 45
Fig 10.4.3
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Fig 10.4.4
Section 10.4 Projective Planes 47
Constructing Projective Planes
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Section 10.4 Projective Planes 49
Fig 10.4.5
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Section 10.5 Affine Planes 51
10.5 AFFINE PLANES
Fig 10.5.1
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Fig 10.5.2
Section 10.5 Affine Planes 53
The Affine Plane AG(2,p)
Fig 10.5.3
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Section 10.5 Affine Planes 55
Fig 10.5.4
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Affine Planes from Projective Planes
Section 10.5 Affine Planes 57
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Section 10.5 Affine Planes 59
Projective Planes from Affine Planes
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Fig 10.5.5
