Generalized Polygons

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Generalized Polygons

Hendrik,van Maldeghem
Generalized Polygons Book PDF

Author : Hendrik,van Maldeghem
Publisher : Birkhäuser
Page : 509 pages
File Size : 48,9 Mb
Release : 2013-11-09
Category : Mathematics
ISBN : 9783034888271

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Generalized Polygons by Hendrik,van Maldeghem Pdf

This book is intended to be an introduction to the fascinating theory ofgeneralized polygons for both the graduate student and the specialized researcher in the field. It gathers together a lot of basic properties (some of which are usually referred to in research papers as belonging to folklore) and very recent and sometimes deep results. I have chosen a fairly strict geometrical approach, which requires some knowledge of basic projective geometry. Yet, it enables one to prove some typically group-theoretical results such as the determination of the automorphism groups of certain Moufang polygons. As such, some basic group-theoretical knowledge is required of the reader. The notion of a generalized polygon is a relatively recent one. But it is one of the most important concepts in incidence geometry. Generalized polygons are the building bricks of Tits buildings. They are the prototypes and precursors of more general geometries such as partial geometries, partial quadrangles, semi-partial ge ometries, near polygons, Moore geometries, etc. The main examples of generalized polygons are the natural geometries associated with groups of Lie type of relative rank 2. This is where group theory comes in and we come to the historical raison d'etre of generalized polygons. In 1959 Jacques Tits discovered the simple groups of type 3D by classifying the 4 trialities with at least one absolute point of a D -geometry. The method was 4 predominantly geometric, and so not surprisingly the corresponding geometries (the twisted triality hexagons) came into play. Generalized hexagons were born.

Generalized Polygons

Hendrik Van Maldeghem
Generalized Polygons Book PDF

Author : Hendrik Van Maldeghem
Publisher : Springer Science & Business Media
Page : 510 pages
File Size : 55,6 Mb
Release : 2012-01-05
Category : Mathematics
ISBN : 9783034802703

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Generalized Polygons by Hendrik Van Maldeghem Pdf

Generalized Polygons is the first book to cover, in a coherent manner, the theory of polygons from scratch. In particular, it fills elementary gaps in the literature and gives an up-to-date account of current research in this area, including most proofs, which are often unified and streamlined in comparison to the versions generally known. Generalized Polygons will be welcomed both by the student seeking an introduction to the subject as well as the researcher who will value the work as a reference. In particular, it will be of great value for specialists working in the field of generalized polygons (which are, incidentally, the rank 2 Tits-buildings) or in fields directly related to Tits-buildings, incidence geometry and finite geometry. The approach taken in the book is of geometric nature, but algebraic results are included and proven (in a geometric way!). A noteworthy feature is that the book unifies and generalizes notions, definitions and results that exist for quadrangles, hexagons, octagons - in the literature very often considered separately - to polygons. Many alternative viewpoints given in the book heighten the sense of beauty of the subject and help to provide further insight into the matter.​

Generalized Polygons

H. van Maldeghem
Generalized Polygons Book PDF

Author : H. van Maldeghem
Publisher : Birkhauser
Page : 502 pages
File Size : 40,5 Mb
Release : 1998-01-01
Category : Mathematics
ISBN : 3764358645

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Generalized Polygons by H. van Maldeghem Pdf

"Generalized Polygons" is the first book to cover, in a coherent manner, the theory of polygons from scratch. In particular, it fills elementary gaps in the literature and gives an up-to-date account of current research in this area, including most proofs, which are often unified and streamlined in comparison to the versions generally known. "Generalized Polygons" will be welcomed both by the student seeking an introduction to the subject as well as the researcher who will value the work as a reference. In particular, it will be of great value for specialists working in the field of generalized polygons (which are, incidentally, the rank 2 Tits-buildings) or in fields directly related to Tits-buildings, incidence geometry and finite geometry. The approach taken in the book is of geometric nature, but algebraic results are included and proven (in a geometric way!). A noteworthy feature is that the book unifies and generalizes notions, definitions and results that exist for quadrangles, hexagons, octagons - in the literature very often considered separately - to polygons. Many alternative viewpoints given in the book heighten the sense of beauty of the subject and help to provide further insight into the matter.

Near Polygons

Bart de Bruyn
Near Polygons Book PDF

Author : Bart de Bruyn
Publisher : Springer Science & Business Media
Page : 268 pages
File Size : 44,5 Mb
Release : 2010-04-11
Category : Mathematics
ISBN : 9783764375539

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Near Polygons by Bart de Bruyn Pdf

Dedicated to the Russian mathematician Albert Shiryaev on his 70th birthday, this is a collection of papers written by his former students, co-authors and colleagues. The book represents the state-of-the-art of a quickly maturing theory and will be an essential source for researchers in this area. The diversity of topics and comprehensive style of the papers make the book attractive for Ph.D. students and young researchers.

Translation Generalized Quadrangles

Joseph A Thas,Koen Thas,Hendrik Van Maldeghem
Translation Generalized Quadrangles Book PDF

Author : Joseph A Thas,Koen Thas,Hendrik Van Maldeghem
Publisher : World Scientific
Page : 377 pages
File Size : 43,5 Mb
Release : 2006-09-28
Category : Mathematics
ISBN : 9789814477284

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Translation Generalized Quadrangles by Joseph A Thas,Koen Thas,Hendrik Van Maldeghem Pdf

Translation generalized quadrangles play a key role in the theory of generalized quadrangles, comparable to the role of translation planes in the theory of projective and affine planes. The notion of translation generalized quadrangle is a local analogue of the more global “Moufang Condition”, a topic of great interest, also due to the classification of all Moufang polygons. Attention is thus paid to recent results in that direction, but also many of the most important results in the general theory of generalized quadrangles that appeared since 1984 are treated.Translation Generalized Quadrangles is essentially self-contained, as the reader is only expected to be familiar with some basic facts on finite generalized quadrangles. Proofs that are either too long or too technical are left out, or just sketched. The three standard works on generalized quadrangles are (co-)authored by the writers of this book: “Finite Generalized Quadrangles” (1984) by S E Payne and J A Thas, “Generalized Polygons” (1998) by H Van Maldeghem, and “Symmetry in Finite Generalized Quadrangles” (2004) by K Thas.

Algebraic Graph Theory

Chris Godsil,Gordon F. Royle
Algebraic Graph Theory Book PDF

Author : Chris Godsil,Gordon F. Royle
Publisher : Springer Science & Business Media
Page : 453 pages
File Size : 43,6 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9781461301639

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Algebraic Graph Theory by Chris Godsil,Gordon F. Royle Pdf

This book presents and illustrates the main tools and ideas of algebraic graph theory, with a primary emphasis on current rather than classical topics. It is designed to offer self-contained treatment of the topic, with strong emphasis on concrete examples.

Finite Geometries

Aart Blokhuis,James W.P. Hirschfeld,Dieter Jungnickel,Joseph A. Thas
Finite Geometries Book PDF

Author : Aart Blokhuis,James W.P. Hirschfeld,Dieter Jungnickel,Joseph A. Thas
Publisher : Springer Science & Business Media
Page : 366 pages
File Size : 48,6 Mb
Release : 2013-12-01
Category : Computers
ISBN : 9781461302834

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Finite Geometries by Aart Blokhuis,James W.P. Hirschfeld,Dieter Jungnickel,Joseph A. Thas Pdf

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.

Robot Motion Planning

Jean-Claude Latombe
Robot Motion Planning Book PDF

Author : Jean-Claude Latombe
Publisher : Springer Science & Business Media
Page : 668 pages
File Size : 47,5 Mb
Release : 2012-12-06
Category : Technology & Engineering
ISBN : 9781461540229

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Robot Motion Planning by Jean-Claude Latombe Pdf

One of the ultimate goals in Robotics is to create autonomous robots. Such robots will accept high-level descriptions of tasks and will execute them without further human intervention. The input descriptions will specify what the user wants done rather than how to do it. The robots will be any kind of versatile mechanical device equipped with actuators and sensors under the control of a computing system. Making progress toward autonomous robots is of major practical inter est in a wide variety of application domains including manufacturing, construction, waste management, space exploration, undersea work, as sistance for the disabled, and medical surgery. It is also of great technical interest, especially for Computer Science, because it raises challenging and rich computational issues from which new concepts of broad useful ness are likely to emerge. Developing the technologies necessary for autonomous robots is a formidable undertaking with deep interweaved ramifications in auto mated reasoning, perception and control. It raises many important prob lems. One of them - motion planning - is the central theme of this book. It can be loosely stated as follows: How can a robot decide what motions to perform in order to achieve goal arrangements of physical objects? This capability is eminently necessary since, by definition, a robot accomplishes tasks by moving in the real world. The minimum one would expect from an autonomous robot is the ability to plan its x Preface own motions.

Points and Lines

Ernest E. Shult
Points and Lines Book PDF

Author : Ernest E. Shult
Publisher : Springer Science & Business Media
Page : 682 pages
File Size : 46,5 Mb
Release : 2010-12-13
Category : Mathematics
ISBN : 9783642156274

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Points and Lines by Ernest E. Shult Pdf

The classical geometries of points and lines include not only the projective and polar spaces, but similar truncations of geometries naturally arising from the groups of Lie type. Virtually all of these geometries (or homomorphic images of them) are characterized in this book by simple local axioms on points and lines. Simple point-line characterizations of Lie incidence geometries allow one to recognize Lie incidence geometries and their automorphism groups. These tools could be useful in shortening the enormously lengthy classification of finite simple groups. Similarly, recognizing ruled manifolds by axioms on light trajectories offers a way for a physicist to recognize the action of a Lie group in a context where it is not clear what Hamiltonians or Casimir operators are involved. The presentation is self-contained in the sense that proofs proceed step-by-step from elementary first principals without further appeal to outside results. Several chapters have new heretofore unpublished research results. On the other hand, certain groups of chapters would make good graduate courses. All but one chapter provide exercises for either use in such a course, or to elicit new research directions.

Buildings, Finite Geometries and Groups

N.S. Narasimha Sastry
Buildings Finite Geometries and Groups Book PDF

Author : N.S. Narasimha Sastry
Publisher : Springer Science & Business Media
Page : 348 pages
File Size : 50,9 Mb
Release : 2011-11-13
Category : Mathematics
ISBN : 9781461407096

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Buildings, Finite Geometries and Groups by N.S. Narasimha Sastry Pdf

This is the Proceedings of the ICM 2010 Satellite Conference on “Buildings, Finite Geometries and Groups” organized at the Indian Statistical Institute, Bangalore, during August 29 – 31, 2010. This is a collection of articles by some of the currently very active research workers in several areas related to finite simple groups, Chevalley groups and their generalizations: theory of buildings, finite incidence geometries, modular representations, Lie theory, etc. These articles reflect the current major trends in research in the geometric and combinatorial aspects of the study of these groups. The unique perspective the authors bring in their articles on the current developments and the major problems in their area is expected to be very useful to research mathematicians, graduate students and potential new entrants to these areas.

Combinatorics

M. Hall Jr.,J.H. van Lint
Combinatorics Book PDF

Author : M. Hall Jr.,J.H. van Lint
Publisher : Springer Science & Business Media
Page : 480 pages
File Size : 44,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401018265

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Combinatorics by M. Hall Jr.,J.H. van Lint Pdf

Combinatorics has come of age. It had its beginnings in a number of puzzles which have still not lost their charm. Among these are EULER'S problem of the 36 officers and the KONIGSBERG bridge problem, BACHET's problem of the weights, and the Reverend T.P. KIRKMAN'S problem of the schoolgirls. Many of the topics treated in ROUSE BALL'S Recreational Mathe matics belong to combinatorial theory. All of this has now changed. The solution of the puzzles has led to a large and sophisticated theory with many complex ramifications. And it seems probable that the four color problem will only be solved in terms of as yet undiscovered deep results in graph theory. Combinatorics and the theory of numbers have much in common. In both theories there are many prob lems which are easy to state in terms understandable by the layman, but whose solution depends on complicated and abstruse methods. And there are now interconnections between these theories in terms of which each enriches the other. Combinatorics includes a diversity of topics which do however have interrelations in superficially unexpected ways. The instructional lectures included in these proceedings have been divided into six major areas: 1. Theory of designs; 2. Graph theory; 3. Combinatorial group theory; 4. Finite geometry; 5. Foundations, partitions and combinatorial geometry; 6. Coding theory. They are designed to give an overview of the classical foundations of the subjects treated and also some indication of the present frontiers of research.

General Galois Geometries

James Hirschfeld,Joseph A. Thas
General Galois Geometries Book PDF

Author : James Hirschfeld,Joseph A. Thas
Publisher : Springer
Page : 409 pages
File Size : 43,5 Mb
Release : 2016-02-03
Category : Mathematics
ISBN : 9781447167907

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General Galois Geometries by James Hirschfeld,Joseph A. Thas Pdf

This book is the second edition of the third and last volume of a treatise on projective spaces over a finite field, also known as Galois geometries. This volume completes the trilogy comprised of plane case (first volume) and three dimensions (second volume). This revised edition includes much updating and new material. It is a mostly self-contained study of classical varieties over a finite field, related incidence structures and particular point sets in finite n-dimensional projective spaces. General Galois Geometries is suitable for PhD students and researchers in combinatorics and geometry. The separate chapters can be used for courses at postgraduate level.

LEDA

Kurt Mehlhorn,Stefan Näher
LEDA Book PDF

Author : Kurt Mehlhorn,Stefan Näher
Publisher : Cambridge University Press
Page : 1050 pages
File Size : 53,8 Mb
Release : 1999-11-11
Category : Computers
ISBN : 0521563291

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LEDA by Kurt Mehlhorn,Stefan Näher Pdf

LEDA is a library of efficient data types and algorithms and a platform for combinatorial and geometric computing on which application programs can be built. In each of the core computer science areas of data structures, graph and network algorithms, and computational geometry, LEDA covers all (and more) that is found in the standard textbooks. LEDA is the first such library; it is written in C++ and is available on many types of machine. Whilst the software is freely available worldwide and is installed at hundreds of sites, this is the first book devoted to the library. Written by the main authors of LEDA, it is the definitive account, describing how the system is constructed and operates and how it can be used. The authors supply ample examples from a range of areas to show how the library can be used in practice, making the book essential for all workers in algorithms, data structures and computational geometry.

Handbook of Combinatorics

R.L. Graham
Handbook of Combinatorics Book PDF

Author : R.L. Graham
Publisher : Elsevier
Page : 2404 pages
File Size : 52,7 Mb
Release : 1995-12-11
Category : Computers
ISBN : 9780080933849

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Handbook of Combinatorics by R.L. Graham Pdf

Handbook of Combinatorics

Moufang Polygons

Jacques Tits,Richard M. Weiss
Moufang Polygons Book PDF

Author : Jacques Tits,Richard M. Weiss
Publisher : Springer Science & Business Media
Page : 529 pages
File Size : 46,6 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9783662046890

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Moufang Polygons by Jacques Tits,Richard M. Weiss Pdf

This book gives the complete classification of Moufang polygons, starting from first principles. In particular, it may serve as an introduction to the various important algebraic concepts which arise in this classification including alternative division rings, quadratic Jordan division algebras of degree three, pseudo-quadratic forms, BN-pairs and norm splittings of quadratic forms. This book also contains a new proof of the classification of irreducible spherical buildings of rank at least three based on the observation that all the irreducible rank two residues of such a building are Moufang polygons. In an appendix, the connection between spherical buildings and algebraic groups is recalled.