Combinatorics of Finite Geometries

Author: Lynn Margaret Batten

Publisher: Cambridge University Press

ISBN: 9780521599931

Category: Mathematics

Page: 193

View: 3084

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

Author: Albrecht Beutelspacher,F. de Clerck

Publisher: Cambridge University Press

ISBN: 9780521448505

Category: Mathematics

Page: 412

View: 1974

This is a collection of thirty-five articles, covering topics such as finite projective spaces, generalized polygons, strongly regular graphs, diagram geometries, and polar spaces. Contained here are articles from many of the leading practitioners in the field including, for the first time, several distinguished Russian mathematicians. Many of the papers contain important new results and the growing use of computer algebra packages in this area is also demonstrated.
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Finite Geometries and Combinatorial Designs

Proceedings of the AMS Special Session in Finite Geometries and Combinatorial Designs Held October 29-November 1, 1987 [Lincoln, Nebraska]

Author: Earl Sidney Kramer

Publisher: American Mathematical Soc.

ISBN: 0821851187

Category: Mathematics

Page: 312

View: 8091

More than eighty participants from all over the world attended an AMS Special Session on Finite Geometries and Combinatorial Designs held in Lincoln, Nebraska, in the fall of 1987. This volume contains the proceedings of that Special Session, in addition to several invited papers. Employing state-of-the-art combinatorial and geometric methods, the papers show significant advances in this area. Topics range over finite geometry, combinatorial designs, their automorphism groups, and related structures. Requiring graduate-level background, this book is intended primarily for researchers in finite geometries and combinatorial designs. However, the interested nonspecialist will find that the book provides an excellent overview of current activity in these areas.
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Finite Geometry and Combinatorial Applications

Author: Simeon Ball

Publisher: Cambridge University Press

ISBN: 1107107997

Category: Mathematics

Page: 295

View: 2828

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

Author: F. Kárteszi

Publisher: Elsevier

ISBN: 148327814X

Category: Mathematics

Page: 280

View: 4793

North-Holland Texts in Advanced Mathematics: Introduction to Finite Geometries focuses on the advancements in finite geometries, including mapping and combinatorics. The manuscript first offers information on the basic concepts on finite geometries and Galois geometries. Discussions focus on linear mapping of a given quadrangle onto another given quadrangle; point configurations of order 2 on a Galois plane of even order; canonical equation of curves of the second order on the Galois planes of even order; and set of collineations mapping a Galois plane onto itself. The text then ponders on geometrical configurations and nets, as well as pentagon theorem and the Desarguesian configuration, two pentagons inscribed into each other, and the concept of geometrical nets. The publication takes a look at combinatorial applications of finite geometries and combinatorics and finite geometries. Topics include generalizations of the Petersen graph, combinatorial extremal problem, and theorem of closure of the hyperbolic space. The book is a valuable source of data for readers interested in finite geometries.
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Finite Geometries

Reprint of the 1968 Edition

Author: Peter Dembowski

Publisher: Springer Science & Business Media

ISBN: 3642620124

Category: Mathematics

Page: 379

View: 6968

Peter Dembowski was born in Berlin on April 1, 1928. After studying mathematics at the University of Frankfurt of Main, he pursued his graduate studies at Brown Unviersity and the University of Illinois, mainly with R. Baer. Dembowski returned to Frankfurt in 1956. Shortly before his premature death in January 1971, he had been appointed to a chair at the University of Tuebingen. Dembowski taught at the universities of Frankfurt and Tuebingen and - as visiting Professor - in London (Queen Mary College), Rome, and Madison, WI. Dembowski's chief research interest lay in the connections between finite geometries and group theory. His book "Finite Geometries" brought together essentially all that was known at that time about finite geometrical structures, including key results of the author, in a unified and structured perspective. This book became a standard reference as soon as it appeared in 1968. It influenced the expansion of combinatorial geometric research, and left its trace also in neighbouring areas.
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Finite geometries, buildings, and related topics

Author: William M. Kantor

Publisher: Oxford University Press, USA

ISBN: N.A

Category: Mathematics

Page: 159

View: 8376

The theory of buildings was introduced by J. Tits in order to focus on geometric and combinatorial aspects of simple groups of Lie type. Since then, the theory has blossomed into an extremely active field of mathematical research having deep connections with topics as diverse as algebraic groups, arithmetic groups, finite simple groups, and finite geometries, as well as with graph theory and other aspects of combinatorics. This volume is intended to provide an up-to-date survey of the theory of buildings with special emphasis on its interaction with related geometries. Experts in their respective fields provide coverage of such topics as the classification and construction of buildings, finite groups associated with building-like geometries, graphs and associated schemes, and more.
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Projektive Geometrie

Von den Grundlagen bis zu den Anwendungen

Author: Albrecht Beutelspacher,Ute Rosenbaum

Publisher: Springer-Verlag

ISBN: 3322968901

Category: Mathematics

Page: 229

View: 4562

Dieses Lehrbuch präsentiert projektive Geometrie, ein wichtiges klassisches Gebiet der Mathematik, in neuem Gewand: Ein Akzent liegt auf überraschenden und wichtigen Anwendungen von Geometrie in Codierungstheorie und Kryptographie. Dazu werden alle benötigten Teile der klassischen projektiven Geometrie (synthetische und analytische Geometrie, Quadriken) bereitgestellt. Das Buch ist in moderner mathematischer Sprache geschrieben. Zahlreiche Abbildungen und weit über hundert meist einfache Übungsaufgaben unterstützen das Verständnis des Stoffes. Es eignet sich vorzüglich zum Selbststudium.
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Combinatorics '86

Author: M. Marchi,A. Barlotti,G. Tallini

Publisher: Elsevier

ISBN: 9780080867779

Category: Mathematics

Page: 501

View: 913

Recent developments in all aspects of combinatorial and incidence geometry are covered in this volume, including their links with the foundations of geometry, graph theory and algebraic structures, and the applications to coding theory and computer science. Topics covered include Galois geometries, blocking sets, affine and projective planes, incidence structures and their automorphism groups. Matroids, graph theory and designs are also treated, along with weak algebraic structures such as near-rings, near-fields, quasi-groups, loops, hypergroups etc., and permutation sets and groups. The vitality of combinatorics today lies in its important interactions with computer science. The problems which arise are of a varied nature and suitable techniques to deal with them have to be devised for each situation; one of the special features of combinatorics is the often sporadic nature of solutions, stemming from its links with number theory. The branches of combinatorics are many and various, and all of them are represented in the 56 papers in this volume.
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Finite Geometries

Proceedings of the Fourth Isle of Thorns Conference

Author: Aart Blokhuis,James W.P. Hirschfeld,Dieter Jungnickel,Joseph A. Thas

Publisher: Springer Science & Business Media

ISBN: 1461302838

Category: Computers

Page: 368

View: 4347

When? These are the proceedings of Finite Geometries, the Fourth Isle of Thorns Conference, which took place from Sunday 16 to Friday 21 July, 2000. It was organised by the editors of this volume. The Third Conference in 1990 was published as Advances in Finite Geometries and Designs by Oxford University Press and the Second Conference in 1980 was published as Finite Geometries and Designs by Cambridge University Press. The main speakers were A. R. Calderbank, P. J. Cameron, C. E. Praeger, B. Schmidt, H. Van Maldeghem. There were 64 participants and 42 contributions, all listed at the end of the volume. Conference web site http://www. maths. susx. ac. uk/Staff/JWPH/ Why? This collection of 21 articles describes the latest research and current state of the art in the following inter-linked areas: • combinatorial structures in finite projective and affine spaces, also known as Galois geometries, in which combinatorial objects such as blocking sets, spreads and partial spreads, ovoids, arcs and caps, as well as curves and hypersurfaces, are all of interest; • geometric and algebraic coding theory; • finite groups and incidence geometries, as in polar spaces, gener alized polygons and diagram geometries; • algebraic and geometric design theory, in particular designs which have interesting symmetric properties and difference sets, which play an important role, because of their close connections to both Galois geometry and coding theory.
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Advanced Combinatorics

The Art of Finite and Infinite Expansions

Author: Louis Comtet

Publisher: Springer Science & Business Media

ISBN: 9401021961

Category: Mathematics

Page: 343

View: 3676

Notwithstanding its title, the reader will not find in this book a systematic account of this huge subject. Certain classical aspects have been passed by, and the true title ought to be "Various questions of elementary combina torial analysis". For instance, we only touch upon the subject of graphs and configurations, but there exists a very extensive and good literature on this subject. For this we refer the reader to the bibliography at the end of the volume. The true beginnings of combinatorial analysis (also called combina tory analysis) coincide with the beginnings of probability theory in the 17th century. For about two centuries it vanished as an autonomous sub ject. But the advance of statistics, with an ever-increasing demand for configurations as well as the advent and development of computers, have, beyond doubt, contributed to reinstating this subject after such a long period of negligence. For a long time the aim of combinatorial analysis was to count the different ways of arranging objects under given circumstances. Hence, many of the traditional problems of analysis or geometry which are con cerned at a certain moment with finite structures, have a combinatorial character. Today, combinatorial analysis is also relevant to problems of existence, estimation and structuration, like all other parts of mathema tics, but exclusively forjinite sets.
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Combinatorics '90

Recent Trends and Applications

Author: A. Barlotti,A. Bichara,P.V. Ceccherini,G. Tallini

Publisher: Elsevier

ISBN: 9780080867922

Category: Mathematics

Page: 565

View: 8537

This volume forms a valuable source of information on recent developments in research in combinatorics, with special regard to the geometric point of view. Topics covered include: finite geometries (arcs, caps, special varieties in a Galois space; generalized quadrangles; Benz planes; foundation of geometry), partial geometries, Buekenhout geometries, transitive permutation sets, flat-transitive geometries, design theory, finite groups, near-rings and semifields, MV-algebras, coding theory, cryptography and graph theory in its geometric and design aspects.
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Mostly Finite Geometries

Author: Norman Johnson

Publisher: CRC Press

ISBN: 9780824700355

Category: Mathematics

Page: 456

View: 9716

Based on the proceedings of the conference held at the University of Iowa, in honour and celebration of the mathematician T.G. Ostrom's 80th birthday, this text focuses on finite geometries as well as topological geometries in the infinite case, some of which originate with ideas of finite geometric objects. It includes information about flocks of quadratic cones and related geometric and combinatorial structures.
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Surveys in Combinatorics, 1997

Author: British Combinatorial Conference

Publisher: Cambridge University Press

ISBN: 9780521598408

Category: Mathematics

Page: 338

View: 3997

The invited lectures given at the 16th. British Combinatorial Conference, July 1997 at Queen Mary and Westfield College.
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Combinatorics of Symmetric Designs

Author: Yury J. Ionin,Mohan S. Shrikhande

Publisher: Cambridge University Press

ISBN: 1139449664

Category: Mathematics

Page: N.A

View: 9009

The aim of this book is to provide a unified exposition of the theory of symmetric designs with emphasis on recent developments. The authors cover the combinatorial aspects of the theory giving particular attention to the construction of symmetric designs and related objects. The last five chapters of the book are devoted to balanced generalized weighing matrices, decomposable symmetric designs, subdesigns of symmetric designs, non-embeddable quasi-residual designs, and Ryser designs. Most results in these chapters have never previously appeared in book form. The book concludes with a comprehensive bibliography of over 400 entries. Researchers in all areas of combinatorial designs, including coding theory and finite geometries, will find much of interest here. Detailed proofs and a large number of exercises make this book suitable as a text for an advanced course in combinatorial designs.
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Hypergraphs

Combinatorics of Finite Sets

Author: C. Berge

Publisher: Elsevier

ISBN: 9780080880235

Category: Mathematics

Page: 254

View: 7785

Graph Theory has proved to be an extremely useful tool for solving combinatorial problems in such diverse areas as Geometry, Algebra, Number Theory, Topology, Operations Research and Optimization. It is natural to attempt to generalise the concept of a graph, in order to attack additional combinatorial problems. The idea of looking at a family of sets from this standpoint took shape around 1960. In regarding each set as a ``generalised edge'' and in calling the family itself a ``hypergraph'', the initial idea was to try to extend certain classical results of Graph Theory such as the theorems of Turán and König. It was noticed that this generalisation often led to simplification; moreover, one single statement, sometimes remarkably simple, could unify several theorems on graphs. This book presents what seems to be the most significant work on hypergraphs.
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Finite Geometries

Author: Baker

Publisher: CRC Press

ISBN: 9780824774882

Category: Mathematics

Page: 400

View: 3143

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