Author: Neil White

Publisher: Cambridge University Press

ISBN: 9780521333399

Category: Mathematics

Page: 212

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### Combinatorial Geometries

This book is a continuation of Theory of Matroids (also edited by Neil White), and again consists of a series of related surveys that have been contributed by authorities in the area. The volume begins with three chapters on coordinatisations, followed by one on matching theory. The next two deal with transversal and simplicial matroids. These are followed by studies of the important matroid invariants. The final chapter deals with matroids in combinatorial optimisation, a topic of much current interest. The whole volume has been carefully edited to ensure a uniform style and notation throughout, and to make a work that can be used as a reference or as an introductory textbook for graduate students or non-specialists.

### On the foundations of combinatorial theory: combinatorial geometries

A major aim of this book is to present the theory of combinatorial geometry in a form accessible to mathematicians working in disparate subjects.

### Matroids and combinatorial geometries

### Combinatorial Geometry with Applications to Field Theory

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.

### Combinatorial Geometry with Applications to Field Theory, Second Edition, graduate textbook in mathematics

### Algorithms in Combinatorial Geometry

This book offers a modern approach to computational geo- metry, an area thatstudies the computational complexity of geometric problems. Combinatorial investigations play an important role in this study.

### Geometry, Perspective Drawing, and Mechanisms

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.

### Theory of Matroids

The theory of matroids is unique in the extent to which it connects such disparate branches of combinatorial theory and algebra as graph theory, lattice theory, design theory, combinatorial optimization, linear algebra, group theory, ring theory and field theory. Furthermore, matroid theory is alone among mathematical theories because of the number and variety of its equivalent axiom systems. Indeed, matroids are amazingly versatile and the approaches to the subject are varied and numerous. This book is a primer in the basic axioms and constructions of matroids. The contributions by various leaders in the field include chapters on axiom systems, lattices, basis exchange properties, orthogonality, graphs and networks, constructions, maps, semi-modular functions and an appendix on cryptomorphisms. The authors have concentrated on giving a lucid exposition of the individual topics; explanations of theorems are preferred to complete proofs and original work is thoroughly referenced. In addition, exercises are included for each topic.

### Combinatorial Geometry in the Plane

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.

### Geometry and Combinatorics

Geometry and Combinatorics: Selected Works of J. J. Seidel brings together some of the works of J. J. Seidel in geometry and combinatorics. Seidel's selected papers are divided into four areas: graphs and designs; lines with few angles; matrices and forms; and non-Euclidean geometry. A list of all of Seidel's publications is included. Comprised of 29 chapters, this book begins with a discussion on equilateral point sets in elliptic geometry, followed by an analysis of strongly regular graphs of L2-type and of triangular type. The reader is then introduced to strongly regular graphs with (-1, 1, 0) adjacency matrix having eigenvalue 3; graphs related to exceptional root systems; and equiangular lines. Subsequent chapters deal with the regular two-graph on 276 vertices; the congruence order of the elliptic plane; equi-isoclinic subspaces of Euclidean spaces; and Wielandt's visibility theorem. This monograph will be of interest to students and practitioners in the field of mathematics.

### Finite Geometry and Combinatorial Applications

A graduate-level introduction to finite geometry and its applications to other areas of combinatorics.

### Combinatorics of Finite Geometries

Thoroughly revised and updated, with an entirely new chapter on blocking sets in linear spaces.

### Encyclopaedia of Mathematics

This ENCYCLOPAEDIA OF MATHEMATICS aims to be a reference work for all parts of mathematics. It is a translation with updates and editorial comments of the Soviet Mathematical En cyclopaedia published by 'Soviet Encyclopaedia Publishing House' in five volumes in 1977 - 1985. The annotated translation consists of ten volumes including a special index volume. There are three kinds of articles in this ENCYCLOPAEDIA. First of all there are survey-type articles dealing with the various main directions in mathematics (where a rather fine subdivision has been used). The main requirement for these articles has been that they should give a reasonably complete up-to-date account of the current state of affairs in these areas and that they should be maximally accessible. On the whole, these articles should be understandable to mathe matics students in their first specialization years, to graduates from other mathematical areas and, depending on the specific subject, to specialists in other domains of science, engineers and teachers of mathematics. These articles treat their material at a fairly general level and aim to give an idea of the kind of problems, techniques and concepts involved in the area in question. They also contain background and motivation rather than precise statements of precise theorems with detailed definitions and technical details on how to carry out proofs and constructions. The second kind of article, of medium length, contains more detailed concrete problems, results and techniques.

### Geometry, Combinatorial Designs and Related Structures

This volume examines state of the art research in finite geometries and designs.

### A Course in Combinatorics

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.

### Groups Combinatorics & Geometry

Over the past 20 years, the theory of groups in particular simplegroups, finite and algebraic has influenced a number of diverseareas of mathematics. Such areas include topics where groups have beentraditionally applied, such as algebraic combinatorics, finitegeometries, Galois theory and permutation groups, as well as severalmore recent developments.

### Convexity and related combinatorial geometry

### Combinatorics: Graph theory; foundations, partitions, and combinatorial geometry

### Zariski Geometries

This book presents methods and results from the theory of Zariski structures and discusses their applications in geometry as well as various other mathematical fields. Its logical approach helps us understand why algebraic geometry is so fundamental throughout mathematics and why the extension to noncommutative geometry, which has been forced by recent developments in quantum physics, is both natural and necessary. Beginning with a crash course in model theory, this book will suit not only model theorists but also readers with a more classical geometric background.

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Author: Neil White

Publisher: Cambridge University Press

ISBN: 9780521333399

Category: Mathematics

Page: 212

View: 8869

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Publisher: Courier Corporation

ISBN: 0486789969

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Publisher: Academic Press

ISBN: 1483268004

Category: Mathematics

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Publisher: Cambridge University Press

ISBN: 1107107997

Category: Mathematics

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ISBN: 9780521599931

Category: Mathematics

Page: 193

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*C An updated and annotated translation of the Soviet ‘Mathematical Encyclopaedia’*

Author: Michiel Hazewinkel

Publisher: Springer Science & Business Media

ISBN: 940096000X

Category: Mathematics

Page: 508

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Author: J. W. P. Hirschfeld,S. S. Magliveras,M. J. de Resmini

Publisher: Cambridge University Press

ISBN: 9780521595384

Category: Mathematics

Page: 258

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

Publisher: Cambridge University Press

ISBN: 9780521006019

Category: Mathematics

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*Durham 2001*

Author: A. A. Ivanov,Martin W. Liebeck,J. Saxl

Publisher: World Scientific

ISBN: 9789812564481

Category: Combinatorial analysis

Page: 335

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*proceedings of the second University of Oklahoma conference*

Author: David C. Kay,Marilyn Breen,University of Oklahoma

Publisher: Marcel Dekker Inc

ISBN: N.A

Category: Mathematics

Page: 243

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Author: Marshall Hall,Jacobus Hendricus van Lint

Publisher: N.A

ISBN: N.A

Category: Combinatorial analysis

Page: 120

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*Geometry from the Logician's Point of View*

Author: Boris Zilber

Publisher: Cambridge University Press

ISBN: 1139486519

Category: Mathematics

Page: N.A

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