Extremal Combinatorics With Applications in Computer Science /
This book is a concise, self-contained, up-to-date introduction to extremal combinatorics for nonspecialists. There is a strong emphasis on theorems with particularly elegant and informative proofs, they may be called gems of the theory. The author presents a wide spectrum of the most powerful combi...
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| Format: | Electronisk eBog |
| Sprog: | English |
| Udgivet: |
Berlin, Heidelberg :
Springer Berlin Heidelberg : Imprint: Springer,
2011.
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| Udgivelse: | 2nd ed. 2011. |
| Serier: | Texts in Theoretical Computer Science. An EATCS Series,
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| Fag: | |
| Online adgang: | https://doi.org/10.1007/978-3-642-17364-6 |
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Indholdsfortegnelse:
- Preface
- Prolog: What this Book Is About
- Notation
- Counting
- Advanced Counting
- Probabilistic Counting
- The Pigeonhole Principle
- Systems of Distinct Representatives
- Sunflowers
- Intersecting Families
- Chains and Antichains
- Blocking Sets and the Duality
- Density and Universality
- Witness Sets and Isolation
- Designs
- The Basic Method
- Orthogonality and Rank Arguments
- Eigenvalues and Graph Expansion
- The Polynomial Method
- Combinatorics of Codes
- Linearity of Expectation
- The Lovász Sieve
- The Deletion Method
- The Second Moment Method
- The Entropy Function
- Random Walks
- Derandomization
- Ramseyan Theorems for Numbers
- The Hales–Jewett Theorem
- Applications in Communications Complexity
- References
- Index.