Extremal Problems For Finite Sets

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Extremal Problems for Finite Sets

Peter Frankl,Norihide Tokushige
Extremal Problems for Finite Sets Book PDF

Author : Peter Frankl,Norihide Tokushige
Publisher : American Mathematical Soc.
Page : 234 pages
File Size : 51,8 Mb
Release : 2018-08-15
Category : Extremal problems
ISBN : 9781470440398

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Extremal Problems for Finite Sets by Peter Frankl,Norihide Tokushige Pdf

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

Daniel Gerbner,Balazs Patkos
Extremal Finite Set Theory Book PDF

Author : Daniel Gerbner,Balazs Patkos
Publisher : CRC Press
Page : 269 pages
File Size : 55,9 Mb
Release : 2018-10-12
Category : Mathematics
ISBN : 9780429804113

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Extremal Finite Set Theory by Daniel Gerbner,Balazs Patkos Pdf

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

Ian Anderson
Combinatorics of Finite Sets Book PDF

Author : Ian Anderson
Publisher : Courier Corporation
Page : 276 pages
File Size : 46,5 Mb
Release : 2002-01-01
Category : Mathematics
ISBN : 0486422577

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Combinatorics of Finite Sets by Ian Anderson Pdf

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.

Theory of Extremal Problems

Anonim
Theory of Extremal Problems Book PDF

Author : Anonim
Publisher : Elsevier
Page : 473 pages
File Size : 49,6 Mb
Release : 2009-06-15
Category : Mathematics
ISBN : 9780080875279

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Theory of Extremal Problems by Anonim Pdf

Theory of Extremal Problems

Homotopy of Extremal Problems

Stanislav V. Emelyanov,Sergey K. Korovin,Nikolai A. Bobylev,Alexander V. Bulatov
Homotopy of Extremal Problems Book PDF

Author : Stanislav V. Emelyanov,Sergey K. Korovin,Nikolai A. Bobylev,Alexander V. Bulatov
Publisher : Walter de Gruyter
Page : 317 pages
File Size : 53,6 Mb
Release : 2011-12-22
Category : Mathematics
ISBN : 9783110893014

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Homotopy of Extremal Problems by Stanislav V. Emelyanov,Sergey K. Korovin,Nikolai A. Bobylev,Alexander V. Bulatov Pdf

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.

Finitely Additive Measures and Relaxations of Extremal Problems

A.G. Chentsov
Finitely Additive Measures and Relaxations of Extremal Problems Book PDF

Author : A.G. Chentsov
Publisher : Springer Science & Business Media
Page : 261 pages
File Size : 50,9 Mb
Release : 1996-09-30
Category : Language Arts & Disciplines
ISBN : 9780306110382

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Finitely Additive Measures and Relaxations of Extremal Problems by A.G. Chentsov Pdf

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.

Algebraic, Extremal and Metric Combinatorics 1986

M. Deza,Peter Frankl,I. G. Rosenberg
Algebraic Extremal and Metric Combinatorics 1986 Book PDF

Author : M. Deza,Peter Frankl,I. G. Rosenberg
Publisher : Cambridge University Press
Page : 260 pages
File Size : 52,6 Mb
Release : 1988-08-25
Category : Mathematics
ISBN : 0521359236

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Algebraic, Extremal and Metric Combinatorics 1986 by M. Deza,Peter Frankl,I. G. Rosenberg Pdf

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.

Contemporary Trends in Discrete Mathematics

Ronald L. Graham
Contemporary Trends in Discrete Mathematics Book PDF

Author : Ronald L. Graham
Publisher : American Mathematical Soc.
Page : 412 pages
File Size : 40,9 Mb
Release : 1999-01-01
Category : Mathematics
ISBN : 0821885812

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Contemporary Trends in Discrete Mathematics by Ronald L. Graham Pdf

Discrete mathematics stands among the leading disciplines of mathematics and theoretical computer science. This is due primarily to its increasing role in university curriculae and its growing importance in applications ranging from optimization to molecular biology. An inaugural conference was held cooperatively by DIMATIA and DIMACS to focus on the versatility, width, and depth of current progress in the subject area. This volume offers a well-balanced blend of research and survey papers reflecting the exciting, attractive topics in contemporary discrete mathematics. Discussed in the book are topics such as graph theory, partially ordered sets, geometrical Ramsey theory, computational complexity issues and applications.

Finite and Infinite Sets

A. Hajnal,L. Lovász,V. T. Sós
Finite and Infinite Sets Book PDF

Author : A. Hajnal,L. Lovász,V. T. Sós
Publisher : Elsevier
Page : 439 pages
File Size : 50,5 Mb
Release : 2014-05-15
Category : Mathematics
ISBN : 9781483161228

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Finite and Infinite Sets by A. Hajnal,L. Lovász,V. T. Sós Pdf

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 Combinatorics

Stasys Jukna
Extremal Combinatorics Book PDF

Author : Stasys Jukna
Publisher : Springer Science & Business Media
Page : 389 pages
File Size : 41,5 Mb
Release : 2013-03-09
Category : Computers
ISBN : 9783662046500

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Extremal Combinatorics by Stasys Jukna Pdf

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.

Sperner Theory

Konrad Engel
Sperner Theory Book PDF

Author : Konrad Engel
Publisher : Cambridge University Press
Page : 430 pages
File Size : 43,6 Mb
Release : 1997-01-28
Category : Mathematics
ISBN : 9780521452069

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Sperner Theory by Konrad Engel Pdf

The starting point of this book is Sperner's theorem, which answers the question: What is the maximum possible size of a family of pairwise (with respect to inclusion) subsets of a finite set? This theorem stimulated the development of a fast growing theory dealing with external problems on finite sets and, more generally, on finite partially ordered sets. This book presents Sperner theory from a unified point of view, bringing combinatorial techniques together with methods from programming, linear algebra, Lie-algebra representations and eigenvalue methods, probability theory, and enumerative combinatorics. Researchers and graduate students in discrete mathematics, optimisation, algebra, probability theory, number theory, and geometry will find many powerful new methods arising from Sperner theory.

Unsolved Problems in Geometry

Hallard T. Croft,K. J. Falconer,Richard K. Guy
Unsolved Problems in Geometry Book PDF

Author : Hallard T. Croft,K. J. Falconer,Richard K. Guy
Publisher : New York : Springer-Verlag
Page : 224 pages
File Size : 53,7 Mb
Release : 1991
Category : Mathematics
ISBN : UOM:49015001318923

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Unsolved Problems in Geometry by Hallard T. Croft,K. J. Falconer,Richard K. Guy Pdf

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.

Global Methods for Combinatorial Isoperimetric Problems

L. H. Harper
Global Methods for Combinatorial Isoperimetric Problems Book PDF

Author : L. H. Harper
Publisher : Cambridge University Press
Page : 252 pages
File Size : 53,7 Mb
Release : 2004-02-09
Category : Mathematics
ISBN : 1139452088

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Global Methods for Combinatorial Isoperimetric Problems by L. H. Harper Pdf

Certain constrained combinatorial optimization problems have a natural analogue in the continuous setting of the classical isoperimetric problem. The study of so called combinatorial isoperimetric problems exploits similarities between these two, seemingly disparate, settings. This text focuses on global methods. This means that morphisms, typically arising from symmetry or direct product decomposition, are employed to transform new problems into more restricted and easily solvable settings whilst preserving essential structure. This book is based on Professor Harper's many years' experience in teaching this subject and is ideal for graduate students entering the field. The author has increased the utility of the text for teaching by including worked examples, exercises and material about applications to computer science. Applied systematically, the global point of view can lead to surprising insights and results, and established researchers will find this to be a valuable reference work on an innovative method for problem solving.

Combinatorics of Finite Sets

Ian Anderson
Combinatorics of Finite Sets Book PDF

Author : Ian Anderson
Publisher : Courier Corporation
Page : 276 pages
File Size : 47,6 Mb
Release : 2012-04-30
Category : Mathematics
ISBN : 9780486143712

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Combinatorics of Finite Sets by Ian Anderson Pdf

Coherent treatment provides comprehensive view of basic methods and results of the combinatorial study of finite set systems. The Clements-Lindstrom extension of the Kruskal-Katona theorem to multisets is explored, as is the Greene-Kleitman result concerning k-saturated chain partitions of general partially ordered sets. Connections with Dilworth's theorem, the marriage problem, and probability are also discussed. Each chapter ends with a helpful series of exercises and outline solutions appear at the end. "An excellent text for a topics course in discrete mathematics." — Bulletin of the American Mathematical Society.

Extended Abstracts EuroComb 2021

Jaroslav Nešetřil,Guillem Perarnau,Juanjo Rué,Oriol Serra
Extended Abstracts EuroComb 2021 Book PDF

Author : Jaroslav Nešetřil,Guillem Perarnau,Juanjo Rué,Oriol Serra
Publisher : Springer Nature
Page : 875 pages
File Size : 42,8 Mb
Release : 2021-08-23
Category : Mathematics
ISBN : 9783030838232

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Extended Abstracts EuroComb 2021 by Jaroslav Nešetřil,Guillem Perarnau,Juanjo Rué,Oriol Serra Pdf

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.