Extremal Problems for Finite Sets

Extremal Problems for Finite Sets

Author: Peter Frankl

Publisher: American Mathematical Soc.

Published: 2018-08-15

Total Pages: 234

ISBN-13: 1470440393

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One of the great appeals of Extremal Set Theory as a subject is that the statements are easily accessible without a lot of mathematical background, yet the proofs and ideas have applications in a wide range of fields including combinatorics, number theory, and probability theory. Written by two of the leading researchers in the subject, this book is aimed at mathematically mature undergraduates, and highlights the elegance and power of this field of study. The first half of the book provides classic results with some new proofs including a complete proof of the Ahlswede-Khachatrian theorem as well as some recent progress on the Erdos matching conjecture. The second half presents some combinatorial structural results and linear algebra methods including the Deza-Erdos-Frankl theorem, application of Rodl's packing theorem, application of semidefinite programming, and very recent progress (obtained in 2016) on the Erdos-Szemeredi sunflower conjecture and capset problem. The book concludes with a collection of challenging open problems.


Book Synopsis Extremal Problems for Finite Sets by : Peter Frankl

Download or read book Extremal Problems for Finite Sets written by Peter Frankl and published by American Mathematical Soc.. This book was released on 2018-08-15 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the great appeals of Extremal Set Theory as a subject is that the statements are easily accessible without a lot of mathematical background, yet the proofs and ideas have applications in a wide range of fields including combinatorics, number theory, and probability theory. Written by two of the leading researchers in the subject, this book is aimed at mathematically mature undergraduates, and highlights the elegance and power of this field of study. The first half of the book provides classic results with some new proofs including a complete proof of the Ahlswede-Khachatrian theorem as well as some recent progress on the Erdos matching conjecture. The second half presents some combinatorial structural results and linear algebra methods including the Deza-Erdos-Frankl theorem, application of Rodl's packing theorem, application of semidefinite programming, and very recent progress (obtained in 2016) on the Erdos-Szemeredi sunflower conjecture and capset problem. The book concludes with a collection of challenging open problems.

Extremal Finite Set Theory

Extremal Finite Set Theory

Author: Daniel Gerbner

Publisher: CRC Press

Published: 2018-10-12

Total Pages: 269

ISBN-13: 0429804113

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Extremal Finite Set Theory surveys old and new results in the area of extremal set system theory. It presents an overview of the main techniques and tools (shifting, the cycle method, profile polytopes, incidence matrices, flag algebras, etc.) used in the different subtopics. The book focuses on the cardinality of a family of sets satisfying certain combinatorial properties. It covers recent progress in the subject of set systems and extremal combinatorics. Intended for graduate students, instructors teaching extremal combinatorics and researchers, this book serves as a sound introduction to the theory of extremal set systems. In each of the topics covered, the text introduces the basic tools used in the literature. Every chapter provides detailed proofs of the most important results and some of the most recent ones, while the proofs of some other theorems are posted as exercises with hints. Features: Presents the most basic theorems on extremal set systems Includes many proof techniques Contains recent developments The book’s contents are well suited to form the syllabus for an introductory course About the Authors: Dániel Gerbner is a researcher at the Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences in Budapest, Hungary. He holds a Ph.D. from Eötvös Loránd University, Hungary and has contributed to numerous publications. His research interests are in extremal combinatorics and search theory. Balázs Patkós is also a researcher at the Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences. He holds a Ph.D. from Central European University, Budapest and has authored several research papers. His research interests are in extremal and probabilistic combinatorics.


Book Synopsis Extremal Finite Set Theory by : Daniel Gerbner

Download or read book Extremal Finite Set Theory written by Daniel Gerbner and published by CRC Press. This book was released on 2018-10-12 with total page 269 pages. Available in PDF, EPUB and Kindle. Book excerpt: Extremal Finite Set Theory surveys old and new results in the area of extremal set system theory. It presents an overview of the main techniques and tools (shifting, the cycle method, profile polytopes, incidence matrices, flag algebras, etc.) used in the different subtopics. The book focuses on the cardinality of a family of sets satisfying certain combinatorial properties. It covers recent progress in the subject of set systems and extremal combinatorics. Intended for graduate students, instructors teaching extremal combinatorics and researchers, this book serves as a sound introduction to the theory of extremal set systems. In each of the topics covered, the text introduces the basic tools used in the literature. Every chapter provides detailed proofs of the most important results and some of the most recent ones, while the proofs of some other theorems are posted as exercises with hints. Features: Presents the most basic theorems on extremal set systems Includes many proof techniques Contains recent developments The book’s contents are well suited to form the syllabus for an introductory course About the Authors: Dániel Gerbner is a researcher at the Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences in Budapest, Hungary. He holds a Ph.D. from Eötvös Loránd University, Hungary and has contributed to numerous publications. His research interests are in extremal combinatorics and search theory. Balázs Patkós is also a researcher at the Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences. He holds a Ph.D. from Central European University, Budapest and has authored several research papers. His research interests are in extremal and probabilistic combinatorics.

Combinatorics of Finite Sets

Combinatorics of Finite Sets

Author: Ian Anderson

Publisher: Courier Corporation

Published: 2002-01-01

Total Pages: 276

ISBN-13: 9780486422572

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Among other subjects explored are the Clements-Lindström extension of the Kruskal-Katona theorem to multisets and the Greene-Kleitmen result concerning k-saturated chain partitions of general partially ordered sets. Includes exercises and solutions.


Book Synopsis Combinatorics of Finite Sets by : Ian Anderson

Download or read book Combinatorics of Finite Sets written by Ian Anderson and published by Courier Corporation. This book was released on 2002-01-01 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: Among other subjects explored are the Clements-Lindström extension of the Kruskal-Katona theorem to multisets and the Greene-Kleitmen result concerning k-saturated chain partitions of general partially ordered sets. Includes exercises and solutions.

Finitely Additive Measures and Relaxations of Extremal Problems

Finitely Additive Measures and Relaxations of Extremal Problems

Author: A.G. Chentsov

Publisher: Springer Science & Business Media

Published: 1996-09-30

Total Pages: 261

ISBN-13: 0306110385

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This monograph constructs correct extensions of extremal problems, including problems of multicriteria optimization as well as more general cone optimization problems. The author obtains common conditions of stability and asymptotic nonsensitivity of extremal problems under perturbation of a part of integral restrictions for finite and infinite systems of restrictions. Features include individual chapters on nonstandard approximation of finitely additive measures by indefinite integrals and constructions of attraction sets. Professor Chentsov illustrates abstract settings by providing examples of problems of impulse control, mathematical programming, and stochastic optimization.


Book Synopsis Finitely Additive Measures and Relaxations of Extremal Problems by : A.G. Chentsov

Download or read book Finitely Additive Measures and Relaxations of Extremal Problems written by A.G. Chentsov and published by Springer Science & Business Media. This book was released on 1996-09-30 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph constructs correct extensions of extremal problems, including problems of multicriteria optimization as well as more general cone optimization problems. The author obtains common conditions of stability and asymptotic nonsensitivity of extremal problems under perturbation of a part of integral restrictions for finite and infinite systems of restrictions. Features include individual chapters on nonstandard approximation of finitely additive measures by indefinite integrals and constructions of attraction sets. Professor Chentsov illustrates abstract settings by providing examples of problems of impulse control, mathematical programming, and stochastic optimization.

Extremal Finite Set Theory

Extremal Finite Set Theory

Author: Daniel Gerbner

Publisher: CRC Press

Published: 2018-10-12

Total Pages: 336

ISBN-13: 0429804121

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Extremal Finite Set Theory surveys old and new results in the area of extremal set system theory. It presents an overview of the main techniques and tools (shifting, the cycle method, profile polytopes, incidence matrices, flag algebras, etc.) used in the different subtopics. The book focuses on the cardinality of a family of sets satisfying certain combinatorial properties. It covers recent progress in the subject of set systems and extremal combinatorics. Intended for graduate students, instructors teaching extremal combinatorics and researchers, this book serves as a sound introduction to the theory of extremal set systems. In each of the topics covered, the text introduces the basic tools used in the literature. Every chapter provides detailed proofs of the most important results and some of the most recent ones, while the proofs of some other theorems are posted as exercises with hints. Features: Presents the most basic theorems on extremal set systems Includes many proof techniques Contains recent developments The book’s contents are well suited to form the syllabus for an introductory course About the Authors: Dániel Gerbner is a researcher at the Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences in Budapest, Hungary. He holds a Ph.D. from Eötvös Loránd University, Hungary and has contributed to numerous publications. His research interests are in extremal combinatorics and search theory. Balázs Patkós is also a researcher at the Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences. He holds a Ph.D. from Central European University, Budapest and has authored several research papers. His research interests are in extremal and probabilistic combinatorics.


Book Synopsis Extremal Finite Set Theory by : Daniel Gerbner

Download or read book Extremal Finite Set Theory written by Daniel Gerbner and published by CRC Press. This book was released on 2018-10-12 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: Extremal Finite Set Theory surveys old and new results in the area of extremal set system theory. It presents an overview of the main techniques and tools (shifting, the cycle method, profile polytopes, incidence matrices, flag algebras, etc.) used in the different subtopics. The book focuses on the cardinality of a family of sets satisfying certain combinatorial properties. It covers recent progress in the subject of set systems and extremal combinatorics. Intended for graduate students, instructors teaching extremal combinatorics and researchers, this book serves as a sound introduction to the theory of extremal set systems. In each of the topics covered, the text introduces the basic tools used in the literature. Every chapter provides detailed proofs of the most important results and some of the most recent ones, while the proofs of some other theorems are posted as exercises with hints. Features: Presents the most basic theorems on extremal set systems Includes many proof techniques Contains recent developments The book’s contents are well suited to form the syllabus for an introductory course About the Authors: Dániel Gerbner is a researcher at the Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences in Budapest, Hungary. He holds a Ph.D. from Eötvös Loránd University, Hungary and has contributed to numerous publications. His research interests are in extremal combinatorics and search theory. Balázs Patkós is also a researcher at the Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences. He holds a Ph.D. from Central European University, Budapest and has authored several research papers. His research interests are in extremal and probabilistic combinatorics.

Algebraic, Extremal and Metric Combinatorics 1986

Algebraic, Extremal and Metric Combinatorics 1986

Author: M. Deza

Publisher: Cambridge University Press

Published: 1988-08-25

Total Pages: 260

ISBN-13: 9780521359238

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This book represents a comprehensive overview of the present state of progress in three related areas of combinatorics. It comprises selected papers from a conference held at the University of Montreal. Topics covered in the articles include association schemes, extremal problems, combinatorial geometrics and matroids, and designs. All the papers contain new results and many are extensive surveys of particular areas of research. Particularly valuable will be Ivanov's paper on recent Soviet research in these areas. Consequently this volume will be of great attraction to all researchers in combinatorics and to research students requiring a rapid introduction to some of the open problems in the subject.


Book Synopsis Algebraic, Extremal and Metric Combinatorics 1986 by : M. Deza

Download or read book Algebraic, Extremal and Metric Combinatorics 1986 written by M. Deza and published by Cambridge University Press. This book was released on 1988-08-25 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book represents a comprehensive overview of the present state of progress in three related areas of combinatorics. It comprises selected papers from a conference held at the University of Montreal. Topics covered in the articles include association schemes, extremal problems, combinatorial geometrics and matroids, and designs. All the papers contain new results and many are extensive surveys of particular areas of research. Particularly valuable will be Ivanov's paper on recent Soviet research in these areas. Consequently this volume will be of great attraction to all researchers in combinatorics and to research students requiring a rapid introduction to some of the open problems in the subject.

Homotopy of Extremal Problems

Homotopy of Extremal Problems

Author: Stanislav V. Emelyanov

Publisher: Walter de Gruyter

Published: 2011-12-22

Total Pages: 317

ISBN-13: 3110893010

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This monograph provides a thorough treatment of parameter-dependent extremal problems with local minimum values that remain unchanged under changes of the parameter. The authors consider the theory as well the practical treatment of those problems, both in finite-dimensional as well as in infinite-dimensional spaces. Various applications are considered, e.g., variational calculus, control theory and bifurcations theory. Thorough treatment of parameter-dependent extremal problems with local minimum values. Includes many applications, e.g., variational calculus, control theory and bifurcations theory. Intended for specialists in the field of nonlinear analysis and its applications as well as for students specializing in these subjects.


Book Synopsis Homotopy of Extremal Problems by : Stanislav V. Emelyanov

Download or read book Homotopy of Extremal Problems written by Stanislav V. Emelyanov and published by Walter de Gruyter. This book was released on 2011-12-22 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph provides a thorough treatment of parameter-dependent extremal problems with local minimum values that remain unchanged under changes of the parameter. The authors consider the theory as well the practical treatment of those problems, both in finite-dimensional as well as in infinite-dimensional spaces. Various applications are considered, e.g., variational calculus, control theory and bifurcations theory. Thorough treatment of parameter-dependent extremal problems with local minimum values. Includes many applications, e.g., variational calculus, control theory and bifurcations theory. Intended for specialists in the field of nonlinear analysis and its applications as well as for students specializing in these subjects.

Theory of Extremal Problems

Theory of Extremal Problems

Author:

Publisher: Elsevier

Published: 2009-06-15

Total Pages: 473

ISBN-13: 0080875270

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Theory of Extremal Problems


Book Synopsis Theory of Extremal Problems by :

Download or read book Theory of Extremal Problems written by and published by Elsevier. This book was released on 2009-06-15 with total page 473 pages. Available in PDF, EPUB and Kindle. Book excerpt: Theory of Extremal Problems

Extremal Combinatorics

Extremal Combinatorics

Author: Stasys Jukna

Publisher: Springer Science & Business Media

Published: 2013-03-09

Total Pages: 389

ISBN-13: 3662046504

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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.


Book Synopsis Extremal Combinatorics by : Stasys Jukna

Download or read book Extremal Combinatorics written by Stasys Jukna and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Unsolved Problems in Geometry

Unsolved Problems in Geometry

Author: Hallard T. Croft

Publisher: New York : Springer-Verlag

Published: 1991

Total Pages: 224

ISBN-13:

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For mathematicians or others who wish to keep up to date with the state of the art of geometrical problems, this collection of problems that are easy to state and understand but are as yet unsolved covers a wide variety of topics including convex sets, polyhedra, packing and covering, tiling, and combinatorial problems. Annotation copyrighted by Book News, Inc., Portland, OR.


Book Synopsis Unsolved Problems in Geometry by : Hallard T. Croft

Download or read book Unsolved Problems in Geometry written by Hallard T. Croft and published by New York : Springer-Verlag. This book was released on 1991 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: For mathematicians or others who wish to keep up to date with the state of the art of geometrical problems, this collection of problems that are easy to state and understand but are as yet unsolved covers a wide variety of topics including convex sets, polyhedra, packing and covering, tiling, and combinatorial problems. Annotation copyrighted by Book News, Inc., Portland, OR.