Extremal Combinatorics
DOWNLOAD
Download Extremal Combinatorics PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Extremal Combinatorics book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
Extremal Combinatorics
DOWNLOAD
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 Combinatorics
DOWNLOAD
Author : Stasys Jukna
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
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 2013-03-09 with Computers categories.
Combinatorial mathematics has been pursued since time immemorial, and at a reasonable scientific level at least since Leonhard Euler (1707-1783). It ren dered many services to both pure and applied mathematics. Then along came the prince of computer science with its many mathematical problems and needs - and it was combinatorics that best fitted the glass slipper held out. Moreover, it has been gradually more and more realized that combinatorics has all sorts of deep connections with "mainstream areas" of mathematics, such as algebra, geometry and probability. This is why combinatorics is now apart of the standard mathematics and computer science curriculum. This book is as an introduction to extremal combinatorics - a field of com binatorial mathematics which has undergone aperiod of spectacular growth in recent decades. The word "extremal" comes from the nature of problems this field deals with: if a collection of finite objects (numbers, graphs, vectors, sets, etc. ) satisfies certain restrictions, how large or how small can it be? For example, how many people can we invite to a party where among each three people there are two who know each other and two who don't know each other? An easy Ramsey-type argument shows that at most five persons can attend such a party. Or, suppose we are given a finite set of nonzero integers, and are asked to mark an as large as possible subset of them under the restriction that the sum of any two marked integers cannot be marked.
Extremal Finite Set Theory
DOWNLOAD
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
DOWNLOAD
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.
Higher Order Combinatorics For Scholars
DOWNLOAD
Author : Pasquale De Marco
language : en
Publisher: Pasquale De Marco
Release Date : 2025-07-10
Higher Order Combinatorics For Scholars written by Pasquale De Marco and has been published by Pasquale De Marco this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-07-10 with Mathematics categories.
**Higher-Order Combinatorics for Scholars** is a comprehensive introduction to higher-order combinatorics, suitable for advanced undergraduates and graduate students in mathematics, computer science, and engineering. It provides a rigorous and systematic treatment of the fundamental concepts and techniques of combinatorics, with a focus on applications to other areas of mathematics, such as graph theory, number theory, probability theory, linear algebra, optimization, complexity theory, and algorithmic combinatorics. The book is divided into ten chapters, each of which covers a different aspect of combinatorics. The first chapter introduces the basic counting principles, as well as more advanced topics such as generating functions and the inclusion-exclusion principle. The second chapter covers advanced counting techniques, such as the pigeonhole principle, Ramsey theory, and extremal combinatorics. The third chapter introduces graph theory, which is the study of graphs, which are mathematical structures that consist of a set of vertices and edges. The fourth chapter introduces set theory, which is the study of sets, which are collections of distinct objects. The fifth chapter introduces number theory, which is the study of numbers and their properties. The sixth chapter introduces probability theory, which is the study of the likelihood of events. The seventh chapter introduces linear algebra, which is the study of vectors and matrices. The eighth chapter introduces optimization, which is the study of finding the best possible solution to a given problem. The ninth chapter introduces complexity theory, which is the study of the computational resources required to solve different problems. The tenth chapter introduces algorithmic combinatorics, which is the study of algorithms for solving combinatorial problems. Each chapter contains a wealth of exercises that are designed to help the reader understand the material and to develop problem-solving skills. The book also contains a comprehensive appendix that provides a glossary of terms and a summary of important results. **Higher-Order Combinatorics for Scholars** is a valuable resource for students and researchers who are interested in combinatorics and its applications. It is also a useful reference for anyone who needs to use combinatorial techniques in their work. If you like this book, write a review!
Combinatorics
DOWNLOAD
Author : Pavle Mladenović
language : en
Publisher:
Release Date : 2019
Combinatorics written by Pavle Mladenović and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with Combinatorial analysis categories.
This text provides a theoretical background for several topics in combinatorial mathematics, such as enumerative combinatorics (including partitions and Burnside's lemma), magic and Latin squares, graph theory, extremal combinatorics, mathematical games and elementary probability. A number of examples are given with explanations while the book also provides more than 300 exercises of different levels of difficulty that are arranged at the end of each chapter, and more than 130 additional challenging problems, including problems from mathematical olympiads. Solutions or hints to all exercises and problems are included. The book can be used by secondary school students preparing for mathematical competitions, by their instructors, and by undergraduate students. The book may also be useful for graduate students and for researchers that apply combinatorial methods in different areas.
Combinatorics And Graph Theory A Comprehensive Introduction
DOWNLOAD
Author : Pasquale De Marco
language : en
Publisher: Pasquale De Marco
Release Date : 2025-03-08
Combinatorics And Graph Theory A Comprehensive Introduction written by Pasquale De Marco and has been published by Pasquale De Marco this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-03-08 with Mathematics categories.
Embark on an intellectual journey through the captivating worlds of combinatorics and graph theory with "Combinatorics and Graph Theory: A Comprehensive Introduction." This comprehensive guide unveils the fundamental concepts, theorems, and applications of these interconnected disciplines, empowering readers to solve complex problems and gain a deeper understanding of the underlying patterns and structures that govern our world. Written in a clear and engaging manner, this book is designed for students, researchers, and enthusiasts alike. It begins with an exploration of discrete structures, delving into the intricacies of sets, relations, functions, and counting techniques. Readers are then guided through the fascinating realm of graphs, where they will discover their properties, algorithms, and diverse applications in various fields. As you progress through the chapters, you will encounter a wealth of captivating topics, including Ramsey theory, extremal combinatorics, coding theory, design theory, and much more. Each topic is presented with lucid explanations, insightful examples, and challenging exercises, fostering a deep understanding of the material. "Combinatorics and Graph Theory: A Comprehensive Introduction" is an invaluable resource for anyone seeking to master these fundamental disciplines. Its comprehensive coverage, engaging writing style, and abundance of practice problems make it an ideal companion for students, researchers, and enthusiasts alike. Whether you are seeking a solid foundation in combinatorics and graph theory, delving into the depths of these fields for research purposes, or simply seeking to expand your intellectual horizons, this book is your indispensable guide. Join us on this captivating journey as we unravel the mysteries of combinatorics and graph theory, unlocking new vistas of knowledge and igniting a passion for mathematical exploration. With its comprehensive coverage, clear explanations, and engaging examples, "Combinatorics and Graph Theory: A Comprehensive Introduction" is the ultimate resource for anyone seeking to master these fundamental disciplines. Order your copy today and embark on an intellectual adventure that will transform your understanding of the world around you. If you like this book, write a review!
Lectures On Advances In Combinatorics
DOWNLOAD
Author : Rudolf Ahlswede
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-05-17
Lectures On Advances In Combinatorics written by Rudolf Ahlswede 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 2008-05-17 with Mathematics categories.
The lectures concentrate on highlights in Combinatorial (ChaptersII and III) and Number Theoretical (ChapterIV) Extremal Theory, in particular on the solution of famous problems which were open for many decades. However, the organization of the lectures in six chapters does neither follow the historic developments nor the connections between ideas in several cases. With the speci?ed auxiliary results in ChapterI on Probability Theory, Graph Theory, etc., all chapters can be read and taught independently of one another. In addition to the 16 lectures organized in 6 chapters of the main part of the book, there is supplementary material for most of them in the Appendix. In parti- lar, there are applications and further exercises, research problems, conjectures, and even research programs. The following books and reports [B97], [ACDKPSWZ00], [A01], and [ABCABDM06], mostly of the authors, are frequently cited in this book, especially in the Appendix, and we therefore mark them by short labels as [B], [N], [E], and [G]. We emphasize that there are also “Exercises” in [B], a “Problem Section” with contributions by several authors on pages 1063–1105 of [G], which are often of a combinatorial nature, and “Problems and Conjectures” on pages 172–173 of [E].
Algebraic Extremal And Metric Combinatorics 1986
DOWNLOAD
Author : M. Deza
language : en
Publisher: Cambridge University Press
Release Date : 1988-08-25
Algebraic Extremal And Metric Combinatorics 1986 written by M. Deza and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988-08-25 with Mathematics categories.
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.
DOWNLOAD
Author :
language : en
Publisher: World Scientific
Release Date :
written by and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.