Combinatorial Geometries

Author: Neil White

Publisher: Cambridge University Press

ISBN: 9780521333399

Category: Mathematics

Page: 212

View: 4855

This book is a continuation of Theory of Matroids and again consists of a series of related surveys.

Algorithms in Combinatorial Geometry

Author: Herbert Edelsbrunner

Publisher: Springer Science & Business Media

ISBN: 3642615686

Category: Computers

Page: 423

View: 5556

Computational geometry as an area of research in its own right emerged in the early seventies of this century. Right from the beginning, it was obvious that strong connections of various kinds exist to questions studied in the considerably older field of combinatorial geometry. For example, the combinatorial structure of a geometric problem usually decides which algorithmic method solves the problem most efficiently. Furthermore, the analysis of an algorithm often requires a great deal of combinatorial knowledge. As it turns out, however, the connection between the two research areas commonly referred to as computa tional geometry and combinatorial geometry is not as lop-sided as it appears. Indeed, the interest in computational issues in geometry gives a new and con structive direction to the combinatorial study of geometry. It is the intention of this book to demonstrate that computational and com binatorial investigations in geometry are doomed to profit from each other. To reach this goal, I designed this book to consist of three parts, acorn binatorial part, a computational part, and one that presents applications of the results of the first two parts. The choice of the topics covered in this book was guided by my attempt to describe the most fundamental algorithms in computational geometry that have an interesting combinatorial structure. In this early stage geometric transforms played an important role as they reveal connections between seemingly unrelated problems and thus help to structure the field.

Combinatorial Geometry with Applications to Field Theory

Author: Linfan Mao

Publisher: Infinite Study

ISBN: 1599731002

Category: Combinatorial geometry

Page: 481

View: 3491

This monograph is motivated with surveying mathematics and physics by CC conjecture, i.e., a mathematical science can be reconstructed from or made by combinatorialization. Topics covered in this book include fundamental of mathematical combinatorics, differential Smarandache n-manifolds, combinatorial or differentiable manifolds and submanifolds, Lie multi-groups, combinatorial principal fiber bundles, gravitational field, quantum fields with their combinatorial generalization, also with discussions on fundamental questions in epistemology. All of these are valuable for researchers in combinatorics, topology, differential geometry, gravitational or quantum fields.

Geometry, Perspective Drawing, and Mechanisms

Author: Don Row,Talmage James Reid

Publisher: World Scientific

ISBN: 981434382X

Category: Mathematics

Page: 328

View: 1949

The aim of this book is to examine the geometry of our world and, by blending theory with a variety of every-day examples, to stimulate the imagination of the readers and develop their geometric intuition. It tries to recapture the excitement that surrounded geometry during the Renaissance as the development of perspective drawing gathered pace, or more recently as engineers sought to show that all the world was a machine. The same excitement is here still, as enquiring minds today puzzle over a random-dot stereogram or the interpretation of an image painstakingly transmitted from Jupiter. The book will give a solid foundation for a variety of undergraduate courses, to provide a basis for a geometric component of graduate teacher training, and to provide background for those who work in computer graphics and scene analysis. It begins with a self-contained development of the geometry of extended Euclidean space. This framework is then used to systematically clarify and develop the art of perspective drawing and its converse discipline of scene analysis and to analyze the behavior of bar-and-joint mechanisms and hinged-panel mechanisms. Spherical polyhedra are introduced and scene analysis is applied to drawings of these and associated objects. The book concludes by showing how a natural relaxation of the axioms developed in the early chapters leads to the concept of a matroid and briefly examines some of the attractive properties of these natural structures.

Combinatorial Geometry

Author: János Pach,Pankaj K. Agarwal

Publisher: John Wiley & Sons

ISBN: 1118031369

Category: Mathematics

Page: 376

View: 6308

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

Combinatorial Geometry in the Plane

Author: Hugo Hadwiger,Hans Debrunner,Victor Klee

Publisher: Courier Corporation

ISBN: 0486789969

Category: Mathematics

Page: 128

View: 9554

Advanced undergraduate-level text discusses theorems on topics restricted to the plane, such as convexity, coverings, and graphs. Two-part treatment begins with specific topics followed by an extensive selection of short proofs. 1964 edition.

Combinatorial Geometry and Its Algorithmic Applications

The Alcalá Lectures

Author: János Pach,Micha Sharir,Mîkā Šārîr

Publisher: American Mathematical Soc.

ISBN: 0821846914

Category: Mathematics

Page: 235

View: 316

This book, based on the authors' lecture series at a 2006 satellite meeting of the International Congress of Mathematicians, offers a comprehensive survey of core areas of combinatorial geometry. These lecture notes aptly describe both the history and the state of the art of these topics. These combinatorial techniques have found applications in areas of computer science ranging from graph drawing to frequency allocation in cellular networks.

A Source Book in Matroid Theory

Author: KUNG

Publisher: Springer Science & Business Media

ISBN: 1468491997

Category: Mathematics

Page: 413

View: 1940

by Gian-Carlo Rota The subjects of mathematics, like the subjects of mankind, have finite lifespans, which the historian will record as he freezes history at one instant of time. There are the old subjects, loaded with distinctions and honors. As their problems are solved away and the applications reaped by engineers and other moneymen, ponderous treatises gather dust in library basements, awaiting the day when a generation as yet unborn will rediscover the lost paradise in awe. Then there are the middle-aged subjects. You can tell which they are by roaming the halls of Ivy League universities or the Institute for Advanced Studies. Their high priests haughtily refuse fabulous offers from eager provin cial universities while receiving special permission from the President of France to lecture in English at the College de France. Little do they know that the load of technicalities is already critical, about to crack and submerge their theorems in the dust of oblivion that once enveloped the dinosaurs. Finally, there are the young subjects-combinatorics, for instance. Wild eyed individuals gingerly pick from a mountain of intractable problems, chil dishly babbling the first words of what will soon be a new language. Child hood will end with the first Seminaire Bourbaki. It could be impossible to find a more fitting example than matroid theory of a subject now in its infancy. The telltale signs, for an unfailing diagnosis, are the abundance of deep theorems, going together with a paucity of theories.

A Course in Combinatorics

Author: J. H. van Lint,R. M. Wilson,Richard Michael Wilson

Publisher: Cambridge University Press

ISBN: 9780521006019

Category: Mathematics

Page: 602

View: 6718

This is the second edition of a popular book on combinatorics, a subject dealing with ways of arranging and distributing objects, and which involves ideas from geometry, algebra and analysis. The breadth of the theory is matched by that of its applications, which include topics as diverse as codes, circuit design and algorithm complexity. It has thus become essential for workers in many scientific fields to have some familiarity with the subject. The authors have tried to be as comprehensive as possible, dealing in a unified manner with, for example, graph theory, extremal problems, designs, colorings and codes. The depth and breadth of the coverage make the book a unique guide to the whole of the subject. The book is ideal for courses on combinatorical mathematics at the advanced undergraduate or beginning graduate level. Working mathematicians and scientists will also find it a valuable introduction and reference.

Results and Problems in Combinatorial Geometry

Author: Vladimir G. Boltjansky,Israel Gohberg

Publisher: CUP Archive

ISBN: 9780521269230

Category: Mathematics

Page: 108

View: 5675

In this short book, the authors discuss three types of problems from combinatorial geometry: Borsuk's partition problem, covering convex bodies by smaller homothetic bodies, and the illumination problem. They show how closely related these problems are to each other. The presentation is elementary, with no more than high-school mathematics and an interest in geometry required to follow the arguments. Most of the discussion is restricted to two- and three-dimensional Euclidean space, though sometimes more general results and problems are given. Thus even the mathematically unsophisticated reader can grasp some of the results of a branch of twentieth-century mathematics that has applications in such disciplines as mathematical programming, operations research and theoretical computer science. At the end of the book the authors have collected together a set of unsolved and partially solved problems that a sixth-form student should be able to understand and even attempt to solve.

Combinatorial Geometry and Graph Theory

Indonesia-Japan Joint Conference, IJCCGGT 2003, Bandung, Indonesia, September 13-16, 2003, Revised Selected Papers

Author: Jin Akiyama

Publisher: Springer Science & Business Media

ISBN: 3540244018

Category: Computers

Page: 225

View: 9584

This book constitutes the thoroughly refereed post-proceedings of the Indonesia-Japan Joint Conference on Combinatorial Geometry and Graph Theory, IJCCGGT 2003, held in Bandung, Indonesia in September 2003. The 23 revised papers presented were carefully selected during two rounds of reviewing and improvement. Among the topics covered are coverings, convex polygons, convex polyhedra, matchings, graph colourings, crossing numbers, subdivision numbers, combinatorial optimization, combinatorics, spanning trees, various graph characteristica, convex bodies, labelling, Ramsey number estimation, etc.