Extremal Combinatorial Problems And Their Applications

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Extremal Combinatorics

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Author : Stasys Jukna
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-06-12

Extremal Combinatorics written by Stasys Jukna and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-06-12 with Computers categories.

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.

Extremal Combinatorial Problems And Their Applications

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Author : B. S. Stechkin
language : en
Publisher:
Release Date : 2014-01-15

Extremal Combinatorial Problems And Their Applications written by B. S. Stechkin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.

Extremal Finite Set Theory

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Author : Daniel Gerbner
language : en
Publisher: CRC Press
Release Date : 2018-10-12

Extremal Finite Set Theory written by Daniel Gerbner and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-12 with Mathematics categories.

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.

Extremal Problems For Finite Sets

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Author : Peter Frankl
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-08-15

Extremal Problems For Finite Sets written by Peter Frankl and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-08-15 with Mathematics categories.

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.

Combinatorial Problems In Graph Theory

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Author : N.B. Singh
language : en
Publisher: N.B. Singh
Release Date :

Combinatorial Problems In Graph Theory written by N.B. Singh and has been published by N.B. Singh this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.

"Combinatorial Problems in Graph Theory" offers a comprehensive introduction to the fundamentals of graph theory for beginners. Exploring the fascinating world of graphs, this book covers essential concepts, from basic definitions to advanced applications across diverse fields such as computer science, optimization, and social networks. With clear explanations, practical examples, and engaging problems, it equips readers with the foundational knowledge needed to understand and solve combinatorial problems using graph theory. Ideal for students and enthusiasts alike, this book serves as an accessible entry point into this essential branch of mathematics.

A Primer In Combinatorics

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Author : Alexander Kheyfits
language : en
Publisher: Walter de Gruyter
Release Date : 2010-07-30

A Primer In Combinatorics written by Alexander Kheyfits and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-07-30 with Mathematics categories.

This textbook is devoted to Combinatorics and Graph Theory, which are cornerstones of Discrete Mathematics. Every section begins with simple model problems. Following their detailed analysis, the reader is led through the derivation of definitions, concepts and methods for solving typical problems. Theorems then are formulated, proved and illustrated by more problems of increasing difficulty. Topics covered include elementary combinatorial constructions, application to probability theory, introduction to graphs and trees with application to hierarchical clustering algorithms, more advanced counting techniques, and existence theorems in combinatorial analysis. The text systematically employs the basic language of set theory. This approach is often useful for solving combinatorial problems, especially problems where one has to identify some objects, and significantly reduces the number of the students’ errors; it is demonstrated in the text on many examples. The textbook is suitable for undergraduate and entry-level graduate students of mathematics and computer science, lecturers in these fields, and anyone studying combinatorial methods and graphical models for solving various problems. The book contains more than 700 problems and can be used as a reading and problem book for an independent study seminar or self-education.

A Guide To The Literature On Semirings And Their Applications In Mathematics And Information Sciences

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Author : K. Glazek
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29

A Guide To The Literature On Semirings And Their Applications In Mathematics And Information Sciences written by K. Glazek and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Mathematics categories.

This volume presents a short guide to the extensive literature concerning semir ings along with a complete bibliography. The literature has been created over many years, in variety of languages, by authors representing different schools of mathematics and working in various related fields. In many instances the terminology used is not universal, which further compounds the difficulty of locating pertinent sources even in this age of the Internet and electronic dis semination of research results. So far there has been no single reference that could guide the interested scholar or student to the relevant publications. This book is an attempt to fill this gap. My interest in the theory of semirings began in the early sixties, when to gether with Bogdan W ~glorz I tried to investigate some algebraic aspects of compactifications of topological spaces, semirings of semicontinuous functions, and the general ideal theory for special semirings. (Unfortunately, local alge braists in Poland told me at that time that there was nothing interesting in investigating semiring theory because ring theory was still being developed). However, some time later we became aware of some similar investigations hav ing already been done. The theory of semirings has remained "my first love" ever since, and I have been interested in the results in this field that have been appearing in literature (even though I have not been active in this area myself).

Combinatorial Geometry

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Author : János Pach
language : en
Publisher: John Wiley & Sons
Release Date : 2011-10-18

Combinatorial Geometry written by János Pach and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-10-18 with Mathematics categories.

A complete, self-contained introduction to a powerful and resurgingmathematical discipline . Combinatorial Geometry presents andexplains with complete proofs some of the most important resultsand methods of this relatively young mathematical discipline,started by Minkowski, Fejes Toth, Rogers, and Erd???s. Nearly halfthe results presented in this book were discovered over the pasttwenty years, and most have never before appeared in any monograph.Combinatorial Geometry will be of particular interest tomathematicians, computer scientists, physicists, and materialsscientists interested in computational geometry, robotics, sceneanalysis, and computer-aided design. It is also a superb textbook,complete with end-of-chapter problems and hints to their solutionsthat help students clarify their understanding and test theirmastery of the material. Topics covered include: * Geometric number theory * Packing and covering with congruent convex disks * Extremal graph and hypergraph theory * Distribution of distances among finitely many points * Epsilon-nets and Vapnik--Chervonenkis dimension * Geometric graph theory * Geometric discrepancy theory * And much more

Jordan Real And Lie Structures In Operator Algebras

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Author : Sh. Ayupov
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14

Jordan Real And Lie Structures In Operator Algebras written by Sh. Ayupov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Mathematics categories.

The theory of operator algebras acting on a Hilbert space was initiated in thirties by papers of Murray and von Neumann. In these papers they have studied the structure of algebras which later were called von Neu mann algebras or W* -algebras. They are weakly closed complex *-algebras of operators on a Hilbert space. At present the theory of von Neumann algebras is a deeply developed theory with various applications. In the framework of von Neumann algebras theory the study of fac tors (i.e. W* -algebras with trivial centres) is very important, since they are comparatively simple and investigation of general W* -algebras can be reduced to the case of factors. Therefore the theory of factors is one of the main tools in the structure theory of von Neumann algebras. In the middle of sixtieth Topping [To 1] and Stormer [S 2] have ini tiated the study of Jordan (non associative and real) analogues of von Neumann algebras - so called JW-algebras, i.e. real linear spaces of self adjoint opera.tors on a complex Hilbert space, which contain the identity operator 1. closed with respect to the Jordan (i.e. symmetrised) product INTRODUCTION 2 x 0 y = ~(Xy + yx) and closed in the weak operator topology. The structure of these algebras has happened to be close to the struc ture of von Neumann algebras and it was possible to apply ideas and meth ods similar to von Neumann algebras theory in the study of JW-algebras.

Extremal Graph Theory

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Author : Bela Bollobas
language : en
Publisher: Courier Corporation
Release Date : 2013-07-02

Extremal Graph Theory written by Bela Bollobas and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-07-02 with Mathematics categories.

The ever-expanding field of extremal graph theory encompasses a diverse array of problem-solving methods, including applications to economics, computer science, and optimization theory. This volume, based on a series of lectures delivered to graduate students at the University of Cambridge, presents a concise yet comprehensive treatment of extremal graph theory. Unlike most graph theory treatises, this text features complete proofs for almost all of its results. Further insights into theory are provided by the numerous exercises of varying degrees of difficulty that accompany each chapter. Although geared toward mathematicians and research students, much of Extremal Graph Theory is accessible even to undergraduate students of mathematics. Pure mathematicians will find this text a valuable resource in terms of its unusually large collection of results and proofs, and professionals in other fields with an interest in the applications of graph theory will also appreciate its precision and scope.