Set Systems, Hypergraphs, Families of Vectors, and Combinatorial Probability

Author: Béla Bollobás

Publisher: Cambridge University Press

ISBN: 9780521337038

Category: Mathematics

Page: 177

View: 2202

Combinatorics is a book whose main theme is the study of subsets of a finite set. It gives a thorough grounding in the theories of set systems and hypergraphs, while providing an introduction to matroids, designs, combinatorial probability and Ramsey theory for infinite sets. The gems of the theory are emphasized: beautiful results with elegant proofs. The book developed from a course at Louisiana State University and combines a careful presentation with the informal style of those lectures. It should be an ideal text for senior undergraduates and beginning graduates.

Extremal Combinatorics

With Applications in Computer Science

Author: Stasys Jukna

Publisher: Springer Science & Business Media

ISBN: 3642173640

Category: Computers

Page: 412

View: 3126

This book is a concise, self-contained, up-to-date introduction to extremal combinatorics for nonspecialists. There is a strong emphasis on theorems with particularly elegant and informative proofs, they may be called gems of the theory. The author presents a wide spectrum of the most powerful combinatorial tools together with impressive applications in computer science: methods of extremal set theory, the linear algebra method, the probabilistic method, and fragments of Ramsey theory. No special knowledge in combinatorics or computer science is assumed – the text is self-contained and the proofs can be enjoyed by undergraduate students in mathematics and computer science. Over 300 exercises of varying difficulty, and hints to their solution, complete the text. This second edition has been extended with substantial new material, and has been revised and updated throughout. It offers three new chapters on expander graphs and eigenvalues, the polynomial method and error-correcting codes. Most of the remaining chapters also include new material, such as the Kruskal—Katona theorem on shadows, the Lovász—Stein theorem on coverings, large cliques in dense graphs without induced 4-cycles, a new lower bounds argument for monotone formulas, Dvir's solution of the finite field Kakeya conjecture, Moser's algorithmic version of the Lovász Local Lemma, Schöning's algorithm for 3-SAT, the Szemerédi—Trotter theorem on the number of point-line incidences, surprising applications of expander graphs in extremal number theory, and some other new results.

Extremal Combinatorial Problems and Their Applications

Author: B.S. Stechkin,V.I. Baranov

Publisher: Springer

ISBN: 0585296022

Category: Computers

Page: 210

View: 2319

Combinatorial research has proceeded vigorously in Russia over the last few decades, based on both translated Western sources and original Russian material. The present volume extends the extremal approach to the solution of a large class of problems, including some that were hitherto regarded as exclusively algorithmic, and broadens the choice of theoretical bases for modelling real phenomena in order to solve practical problems. Audience: Graduate students of mathematics and engineering interested in the thematics of extremal problems and in the field of combinatorics in general. Can be used both as a textbook and as a reference handbook.

Computer Recognition Systems

Proceedings of 4th International Conference on Computer Recognition Systems CORES'05

Author: Marek Kurzynski,Edward Puchala,Michal Wozniak,Andrzej Zolnierek

Publisher: Springer Science & Business Media

ISBN: 9783540323907

Category: Computers

Page: 903

View: 9261

th This book contains papers accepted for presentation at the 4 International Conference on Computer Recognition Systems CORES'05, May 22-25, 2005, Rydzyna Castle (Poland), This conference is a continuation of a series of con ferences on similar topics (KOSYR) organized each second year, since 1999, by the Chair of Systems and Computer Networks, Wroclaw University of Tech nology. An increasing interest to those conferences paid not only by home but also by foreign participants inspired the organizers to transform them into conferences of international range. Our expectations that the community of specialists in computer recognizing systems will find CORES'05 a proper form of maintaining the tradition of the former conferences have been confirmed by a large number of submitted papers. Alas, organizational constraints caused a necessity to narrow the acceptance criteria so that only 100 papers have been finally included into the conference program. The area covered by accepted papers is still very large and it shows how vivacious is scientific activity in the domain of computer recognition methods and systems. It contains vari ous theoretical approaches to the recognition problem based on mathematical statistics, fuzzy sets, morphological methods, wavelets, syntactic methods, genetic algorithms, artificial neural networks, ontological models, etc. Most attention is still paid to visual objects recognition; however, acoustic, tex tual and other objects are also considered. Among application areas medical problems are in majority; recognition of faces, speech signals and textual in formation processing methods being also investigated.

Handbook of the Geometry of Banach Spaces

Author: William B. Johnson,Joram Lindenstrauss

Publisher: Elsevier

ISBN: 9780444513052

Category: Mathematics

Page: 1866

View: 6342

Encouraged by new perspectives in Banach space theory, the editors present this second volume that opens with an introductory essay that explains the basics of the theory. The rest of the chapters focus on specific directions of Banach space theory or its applications.

Computing in Euclidean Geometry

Author: Dingzhu Du,Frank Hwang

Publisher: World Scientific

ISBN: 9789810209667

Category: Mathematics

Page: 385

View: 7729

This book is a collection of surveys and exploratory articles about recent developments in the field of computational Euclidean geometry. The topics covered are: a history of Euclidean geometry, Voronoi diagrams, randomized geometric algorithms, computational algebra; triangulations, machine proofs, topological designs, finite-element mesh, computer-aided geometric designs and steiner trees. Each chapter is written by a leading expert in the field and together they provide a clear and authoritative picture of what computational Euclidean geometry is and the direction in which research is going.


Author: N.A

Publisher: N.A



Page: N.A

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Algebra Colloquium

Author: N.A

Publisher: N.A


Category: Algebra

Page: N.A

View: 8115