Extremal Combinatorics (Record no. 75164)
[ view plain ]
| 000 -LEADER | |
|---|---|
| fixed length control field | 04549nam a22005895i 4500 |
| 001 - CONTROL NUMBER | |
| control field | 978-3-642-17364-6 |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20220801140102.0 |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 110831s2011 gw | s |||| 0|eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| ISBN | 9783642173646 |
| -- | 978-3-642-17364-6 |
| 082 04 - CLASSIFICATION NUMBER | |
| Call Number | 004.0151 |
| 100 1# - AUTHOR NAME | |
| Author | Jukna, Stasys. |
| 245 10 - TITLE STATEMENT | |
| Title | Extremal Combinatorics |
| Sub Title | With Applications in Computer Science / |
| 250 ## - EDITION STATEMENT | |
| Edition statement | 2nd ed. 2011. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Number of Pages | XXIV, 412 p. |
| 490 1# - SERIES STATEMENT | |
| Series statement | Texts in Theoretical Computer Science. An EATCS Series, |
| 505 0# - FORMATTED CONTENTS NOTE | |
| Remark 2 | 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. |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc | 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 combinatorial tools together with impressive applications in computer science: methods of extremal set theory, the linear algebra method, the probabilistic method, and fragments of Ramsey theory. No special knowledge in combinatorics or computer science is assumed – the text is self-contained and the proofs can be enjoyed by undergraduate students in mathematics and computer science. Over 300 exercises of varying difficulty, and hints to their solution, complete the text. 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. |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | https://doi.org/10.1007/978-3-642-17364-6 |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) | |
| Koha item type | eBooks |
| 264 #1 - | |
| -- | Berlin, Heidelberg : |
| -- | Springer Berlin Heidelberg : |
| -- | Imprint: Springer, |
| -- | 2011. |
| 336 ## - | |
| -- | text |
| -- | txt |
| -- | rdacontent |
| 337 ## - | |
| -- | computer |
| -- | c |
| -- | rdamedia |
| 338 ## - | |
| -- | online resource |
| -- | cr |
| -- | rdacarrier |
| 347 ## - | |
| -- | text file |
| -- | |
| -- | rda |
| 650 #0 - SUBJECT ADDED ENTRY--SUBJECT 1 | |
| -- | Computer science. |
| 650 #0 - SUBJECT ADDED ENTRY--SUBJECT 1 | |
| -- | Number theory. |
| 650 #0 - SUBJECT ADDED ENTRY--SUBJECT 1 | |
| -- | Computer science—Mathematics. |
| 650 #0 - SUBJECT ADDED ENTRY--SUBJECT 1 | |
| -- | Discrete mathematics. |
| 650 #0 - SUBJECT ADDED ENTRY--SUBJECT 1 | |
| -- | Mathematics—Data processing. |
| 650 14 - SUBJECT ADDED ENTRY--SUBJECT 1 | |
| -- | Theory of Computation. |
| 650 24 - SUBJECT ADDED ENTRY--SUBJECT 1 | |
| -- | Number Theory. |
| 650 24 - SUBJECT ADDED ENTRY--SUBJECT 1 | |
| -- | Discrete Mathematics in Computer Science. |
| 650 24 - SUBJECT ADDED ENTRY--SUBJECT 1 | |
| -- | Discrete Mathematics. |
| 650 24 - SUBJECT ADDED ENTRY--SUBJECT 1 | |
| -- | Computational Mathematics and Numerical Analysis. |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE | |
| -- | 1862-4502 |
| 912 ## - | |
| -- | ZDB-2-SCS |
| 912 ## - | |
| -- | ZDB-2-SXCS |
No items available.