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The Resource Extremal combinatorics : with applications in computer science, Stasys Jukna, (electronic resource)
Extremal combinatorics : with applications in computer science, Stasys Jukna, (electronic resource)
Resource Information
The item Extremal combinatorics : with applications in computer science, Stasys Jukna, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Boston University Libraries.This item is available to borrow from all library branches.
Resource Information
The item Extremal combinatorics : with applications in computer science, Stasys Jukna, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Boston University Libraries.
This item is available to borrow from all library branches.
 Summary
 This book is a concise, selfcontained, uptodate 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 selfcontained 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 errorcorrecting 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 4cycles, 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 3SAT, the Szemerédi—Trotter theorem on the number of pointline incidences, surprising applications of expander graphs in extremal number theory, and some other new results
 Language
 eng
 Edition
 2nd ed.
 Extent
 1 online resource (xxii, 411 p.)
 Contents

 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
 Isbn
 9783642173646
 Label
 Extremal combinatorics : with applications in computer science
 Title
 Extremal combinatorics
 Title remainder
 with applications in computer science
 Statement of responsibility
 Stasys Jukna
 Subject

 Extremal problems (Mathematics)
 Combinatorial analysis
 Electronic books
 Extremal problems (Mathematics)
 Combinatorial analysis
 Combinatorial analysis
 Computer science  Mathematics
 Computer science  Mathematics
 Extremal problems (Mathematics)
 Extremal problems (Mathematics)
 Electronic resources
 Combinatorial analysis
 Extremal problems (Mathematics)
 Extremal problems (Mathematics)
 Informatique
 Computer science  Mathematics
 Computer science  Mathematics
 Computer science  Mathematics
 Combinatorial analysis
 Computer science  Mathematics
 Combinatorial analysis
 Language
 eng
 Summary
 This book is a concise, selfcontained, uptodate 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 selfcontained 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 errorcorrecting 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 4cycles, 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 3SAT, the Szemerédi—Trotter theorem on the number of pointline incidences, surprising applications of expander graphs in extremal number theory, and some other new results
 Cataloging source
 GW5XE
 http://library.link/vocab/creatorDate
 1953
 http://library.link/vocab/creatorName
 Jukna, Stasys
 Image bit depth
 0
 LC call number
 QA164
 LC item number
 .J85 2011
 Literary form
 non fiction
 Nature of contents
 dictionaries
 http://library.link/vocab/relatedWorkOrContributorName
 SpringerLink
 Series statement
 Texts in Theoretical Computer Science. An EATCS Series,
 http://library.link/vocab/subjectName

 Combinatorial analysis
 Extremal problems (Mathematics)
 Computer science
 Combinatorial analysis
 Computer science
 Extremal problems (Mathematics)
 Informatique
 Label
 Extremal combinatorics : with applications in computer science, Stasys Jukna, (electronic resource)
 Antecedent source
 mixed
 Bibliography note
 Includes bibliographical references and index
 Carrier category
 online resource
 Carrier category code
 cr
 Carrier MARC source
 rdacarrier
 Color
 not applicable
 Content category
 text
 Content type code
 txt
 Content type MARC source
 rdacontent
 Contents
 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
 Dimensions
 unknown
 Edition
 2nd ed.
 Extent
 1 online resource (xxii, 411 p.)
 File format
 multiple file formats
 Form of item

 online
 electronic
 Isbn
 9783642173646
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code
 c
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 Stock number
 9783642173639
 System control number

 (OCoLC)756677711
 (OCoLC)ocn756677711
 Label
 Extremal combinatorics : with applications in computer science, Stasys Jukna, (electronic resource)
 Antecedent source
 mixed
 Bibliography note
 Includes bibliographical references and index
 Carrier category
 online resource
 Carrier category code
 cr
 Carrier MARC source
 rdacarrier
 Color
 not applicable
 Content category
 text
 Content type code
 txt
 Content type MARC source
 rdacontent
 Contents
 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
 Dimensions
 unknown
 Edition
 2nd ed.
 Extent
 1 online resource (xxii, 411 p.)
 File format
 multiple file formats
 Form of item

 online
 electronic
 Isbn
 9783642173646
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code
 c
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 Stock number
 9783642173639
 System control number

 (OCoLC)756677711
 (OCoLC)ocn756677711
Subject
 Combinatorial analysis
 Combinatorial analysis
 Combinatorial analysis
 Combinatorial analysis
 Combinatorial analysis
 Combinatorial analysis
 Computer science  Mathematics
 Computer science  Mathematics
 Computer science  Mathematics
 Computer science  Mathematics
 Computer science  Mathematics
 Computer science  Mathematics
 Electronic books
 Electronic resources
 Extremal problems (Mathematics)
 Extremal problems (Mathematics)
 Extremal problems (Mathematics)
 Extremal problems (Mathematics)
 Extremal problems (Mathematics)
 Extremal problems (Mathematics)
 Informatique
Genre
Member of
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