Extremal Combinatorics

With Applications in Computer Science

Authors:

ISBN: 978-3-642-17363-9 (Print) 978-3-642-17364-6 (Online)

Table of contents (27 chapters)

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  1. Front Matter

    Pages I-XXIII

  2. The Classics

    1. Front Matter

      Pages 1-1

    2. No Access

      Book Chapter

      Pages 3-22

      Counting

    3. No Access

      Book Chapter

      Pages 23-39

      Advanced Counting

    4. No Access

      Book Chapter

      Pages 41-51

      Probabilistic Counting

    5. No Access

      Book Chapter

      Pages 53-75

      The Pigeonhole Principle

    6. No Access

      Book Chapter

      Pages 77-86

      Systems of Distinct Representatives

  3. Extremal Set Theory

    1. Front Matter

      Pages 87-87

    2. No Access

      Book Chapter

      Pages 89-98

      Sunflowers

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      Book Chapter

      Pages 99-106

      Intersecting Families

    4. No Access

      Book Chapter

      Pages 107-118

      Chains and Antichains

    5. No Access

      Book Chapter

      Pages 119-134

      Blocking Sets and the Duality

    6. No Access

      Book Chapter

      Pages 135-154

      Density and Universality

    7. No Access

      Book Chapter

      Pages 155-163

      Witness Sets and Isolation

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      Book Chapter

      Pages 165-176

      Designs

  4. The Linear Algebra Method

    1. Front Matter

      Pages 177-177

    2. No Access

      Book Chapter

      Pages 179-196

      The Basic Method

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      Book Chapter

      Pages 197-212

      Orthogonality and Rank Arguments

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      Book Chapter

      Pages 213-222

      Eigenvalues and Graph Expansion

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      Book Chapter

      Pages 223-236

      The Polynomial Method

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      Book Chapter

      Pages 237-251

      Combinatorics of Codes

  5. The Probabilistic Method

    1. Front Matter

      Pages 253-253

    2. No Access

      Book Chapter

      Pages 255-278

      Linearity of Expectation

    3. No Access

      Book Chapter

      Pages 279-291

      The Lovász Sieve

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      Book Chapter

      Pages 293-302

      The Deletion Method

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