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This second edition has been extended with substantial new material, and has been revised and updated throughout. It offers three new chapters on expander graphs and eigenvalues, the polynomial method and error-correcting codes. Most of the remaining chapters also include new material, such as the Kruskal¿Katona theorem on shadows, the Lovász¿Stein theorem on coverings, large cliques in dense graphs without induced 4-cycles, a new lower bounds argument for monotone formulas, Dvir's solution of the finite field Kakeya conjecture, Moser's algorithmic version of the Lovász Local Lemma, Schöning's algorithm for 3-SAT, the Szemerédi¿Trotter theorem on the number of point-line incidences, surprising applications of expander graphs in extremal number theory, and some other new results.
This second edition has been extended with substantial new material, and has been revised and updated throughout. It offers three new chapters on expander graphs and eigenvalues, the polynomial method and error-correcting codes. Most of the remaining chapters also include new material, such as the Kruskal¿Katona theorem on shadows, the Lovász¿Stein theorem on coverings, large cliques in dense graphs without induced 4-cycles, a new lower bounds argument for monotone formulas, Dvir's solution of the finite field Kakeya conjecture, Moser's algorithmic version of the Lovász Local Lemma, Schöning's algorithm for 3-SAT, the Szemerédi¿Trotter theorem on the number of point-line incidences, surprising applications of expander graphs in extremal number theory, and some other new results.
The author is a professor at the Goethe Universität Frankfurt and he is also a member of the Vilnius University Institute of Mathematics and Informatics. His main fields of research are theoretical computer science and discrete mathematics, in particular complexity.
A concise, self-contained, up-to-date introduction to extremal combinatorics for nonspecialists
No special combinatorial or algebraic background is assumed, all necessary elements of linear algebra and discrete probability are introduced
The second edition has been extended with substantial new material, and has been revised and updated throughout
Includes supplementary material: [...]
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.
| Erscheinungsjahr: | 2011 |
|---|---|
| Genre: | Informatik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Buch |
| Seiten: | 436 |
| Reihe: | Texts in Theoretical Computer Science. An EATCS Series |
| Inhalt: |
xxiv
412 S. |
| ISBN-13: | 9783642173639 |
| ISBN-10: | 3642173632 |
| Sprache: | Englisch |
| Herstellernummer: | 80028017 |
| Ausstattung / Beilage: | HC runder Rücken kaschiert |
| Einband: | Gebunden |
| Autor: | Jukna, Stasys |
| Auflage: | 2nd ed. 2011 |
| Hersteller: |
Springer-Verlag GmbH
Springer Berlin Heidelberg Texts in Theoretical Computer Science. An EATCS Series |
| Maße: | 241 x 160 x 29 mm |
| Von/Mit: | Stasys Jukna |
| Erscheinungsdatum: | 02.09.2011 |
| Gewicht: | 0,816 kg |
The author is a professor at the Goethe Universität Frankfurt and he is also a member of the Vilnius University Institute of Mathematics and Informatics. His main fields of research are theoretical computer science and discrete mathematics, in particular complexity.
A concise, self-contained, up-to-date introduction to extremal combinatorics for nonspecialists
No special combinatorial or algebraic background is assumed, all necessary elements of linear algebra and discrete probability are introduced
The second edition has been extended with substantial new material, and has been revised and updated throughout
Includes supplementary material: [...]
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.
| Erscheinungsjahr: | 2011 |
|---|---|
| Genre: | Informatik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Buch |
| Seiten: | 436 |
| Reihe: | Texts in Theoretical Computer Science. An EATCS Series |
| Inhalt: |
xxiv
412 S. |
| ISBN-13: | 9783642173639 |
| ISBN-10: | 3642173632 |
| Sprache: | Englisch |
| Herstellernummer: | 80028017 |
| Ausstattung / Beilage: | HC runder Rücken kaschiert |
| Einband: | Gebunden |
| Autor: | Jukna, Stasys |
| Auflage: | 2nd ed. 2011 |
| Hersteller: |
Springer-Verlag GmbH
Springer Berlin Heidelberg Texts in Theoretical Computer Science. An EATCS Series |
| Maße: | 241 x 160 x 29 mm |
| Von/Mit: | Stasys Jukna |
| Erscheinungsdatum: | 02.09.2011 |
| Gewicht: | 0,816 kg |
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