Extremal Problems For Finite Sets PDF Download
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Author | : Peter Frankl |
Publisher | : American Mathematical Soc. |
Total Pages | : 234 |
Release | : 2018-08-15 |
Genre | : Extremal problems |
ISBN | : 1470440393 |
Download Extremal Problems for Finite Sets Book in PDF, ePub and Kindle
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.
Author | : Daniel Gerbner |
Publisher | : CRC Press |
Total Pages | : 269 |
Release | : 2018-10-12 |
Genre | : Mathematics |
ISBN | : 0429804113 |
Download Extremal Finite Set Theory Book in PDF, ePub and Kindle
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.
Author | : Ian Anderson |
Publisher | : Courier Corporation |
Total Pages | : 276 |
Release | : 2002-01-01 |
Genre | : Mathematics |
ISBN | : 9780486422572 |
Download Combinatorics of Finite Sets Book in PDF, ePub and Kindle
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.
Author | : A.G. Chentsov |
Publisher | : Springer Science & Business Media |
Total Pages | : 261 |
Release | : 1996-09-30 |
Genre | : Language Arts & Disciplines |
ISBN | : 0306110385 |
Download Finitely Additive Measures and Relaxations of Extremal Problems Book in PDF, ePub and Kindle
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.
Author | : Daniel Gerbner |
Publisher | : CRC Press |
Total Pages | : 336 |
Release | : 2018-10-12 |
Genre | : Mathematics |
ISBN | : 0429804121 |
Download Extremal Finite Set Theory Book in PDF, ePub and Kindle
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.
Author | : |
Publisher | : Elsevier |
Total Pages | : 473 |
Release | : 2009-06-15 |
Genre | : Mathematics |
ISBN | : 0080875270 |
Download Theory of Extremal Problems Book in PDF, ePub and Kindle
Theory of Extremal Problems
Author | : Stanislav V. Emelyanov |
Publisher | : Walter de Gruyter |
Total Pages | : 317 |
Release | : 2011-12-22 |
Genre | : Mathematics |
ISBN | : 3110893010 |
Download Homotopy of Extremal Problems Book in PDF, ePub and Kindle
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.
Author | : Stasys Jukna |
Publisher | : Springer Science & Business Media |
Total Pages | : 389 |
Release | : 2013-03-09 |
Genre | : Computers |
ISBN | : 3662046504 |
Download Extremal Combinatorics Book in PDF, ePub and Kindle
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.
Author | : Hallard T. Croft |
Publisher | : New York : Springer-Verlag |
Total Pages | : 224 |
Release | : 1991 |
Genre | : Mathematics |
ISBN | : |
Download Unsolved Problems in Geometry Book in PDF, ePub and Kindle
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.
Author | : Jaroslav Nešetřil |
Publisher | : Springer Nature |
Total Pages | : 875 |
Release | : 2021-08-23 |
Genre | : Mathematics |
ISBN | : 3030838234 |
Download Extended Abstracts EuroComb 2021 Book in PDF, ePub and Kindle
This book collects the extended abstracts of the accepted contributions to EuroComb21. A similar book is published at every edition of EuroComb (every two years since 2001) collecting the most recent advances in combinatorics, graph theory, and related areas. It has a wide audience in the areas, and the papers are used and referenced broadly.