Stasys Jukna
Extremal Combinatorics
Paperback Engels 2010 9783642085598Levertijd ongeveer 9 werkdagen
Gratis verzonden
Samenvatting
This is a concise, up-to-date introduction to extremal combinatorics for non-specialists. Strong emphasis is made on theorems with particularly elegant and informative proofs which may be called the gems of the theory. A wide spectrum of the most powerful combinatorial tools is presented, including methods of extremal set theory, the linear algebra method, the probabilistic method and fragments of Ramsey theory. A thorough discussion of recent applications to computer science illustrates the inherent usefulness of these methods.
Specificaties
ISBN13:9783642085598
Taal:Engels
Bindwijze:Paperback
Aantal pagina's:392
Uitgever:Springer-Verlag Berlin and Heidelberg GmbH & Co. K
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Inhoudsopgave
Introduction.- I. The Classis: Counting.- The Pigeon-Hole Principle.- Principle of Inclusion and Exclusion.- Systems of Distinct Representatives.- Colorings.- Chains and Antichains.- Intersecting Families.- Covers and Transversals.- Sunflowers.- Density and Universality.- Designs.- Witness Sets.- Isolation Lemmas.- II. The Linear Algebra Method: Basic Method.- The Polynomial Technique.- Monotone Span Programs.- III. The Probabilistic Method: Basic Tools.- Counting Sieve.- Lovasz Sieve.- Linearity of Expectation.- The Deletion Method.- Second Moment Method.- Bounding of Large Deviations.- Randomized Algorithms.- Derandomization.- The Entropy Function.- Random Walks and Search Problems.- IV. Fragments of Ramsey Theory: Ramsey's Theorem.- The Hales-Jewett Theorem.- Epilogue: What Next?- Bibliography.- Index.
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