Extremal Problems In Finite Sets

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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.

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 In Finite Sets

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Author : Paulette Lieby
language : en
Publisher:
Release Date : 1999

Extremal Problems In Finite Sets written by Paulette Lieby and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Set theory categories.

Combinatorics Of Finite Sets

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Author : Ian Anderson
language : en
Publisher: Courier Corporation
Release Date : 2002-01-01

Combinatorics Of Finite Sets written by Ian Anderson and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-01-01 with Mathematics categories.

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.

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.

Finite And Infinite Sets

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Author : A. Hajnal
language : en
Publisher: Elsevier
Release Date : 2014-05-15

Finite And Infinite Sets written by A. Hajnal and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-15 with Mathematics categories.

Colloquia Mathematica Societatis Jânos Bolyai, 37: Finite and Infinite Sets, Vol. I focuses on the principles, operations, and approaches involved in finite and infinite sets. The selection first elaborates on essential chains and squares, cellular automata in trees, almost disjoint families of countable sets, and application of Lovasz local lemma. Discussions focus on deleting operations, number of all and self-dual E-chains, transversality of E-chains and E-squares, and binary E-chains and E-squares. The text then elaborates on induced subgraphs, inverse extremal digraph problems, two Sperner-type conditions, and minimal decomposition of all graphs with equinumerous vertices and edges into mutually isomorphic subgraphs. Topics include general digraph extremal problem, matrix graphs and quadratic forms, augmentation of matrices, set of attained densities, proof of the continuity theorem, and inverse extremal multigraph problems. The text examines circular flows in graphs, two-colorings of simple arrangements, monochromatic paths in infinite colored graphs, and graphs associated with an integral domain and their applications. The selection is a dependable reference for researchers interested in finite and infinite sets.

Extremal Problems In Codes Finite Sets And Geometries

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Author : Moya Michelle Mazorow
language : en
Publisher:
Release Date : 1991

Extremal Problems In Codes Finite Sets And Geometries written by Moya Michelle Mazorow and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Electronic dissertations categories.

Extended Abstracts Eurocomb 2021

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Author : Jaroslav Nešetřil
language : en
Publisher: Springer Nature
Release Date : 2021-08-23

Extended Abstracts Eurocomb 2021 written by Jaroslav Nešetřil and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-08-23 with Mathematics categories.

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.

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.

Combinatorics

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Author : Marshall Hall
language : en
Publisher: Taylor & Francis
Release Date : 1975-04-30

Combinatorics written by Marshall Hall and has been published by Taylor & Francis this book supported file pdf, txt, epub, kindle and other format this book has been release on 1975-04-30 with Mathematics categories.

Proceedings of the NATO Advanced Study Institute, Breukelen, The Netherlands, July 8-30, 1974