Flag Transitive Steiner Designs

Author : Michael Huber
Publisher : Springer Science & Business Media
ISBN 13 : 3034600011
Total Pages : 128 pages
Book Rating : 4.19/5 ( download)

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Download or read book Flag-transitive Steiner Designs written by Michael Huber and published by Springer Science & Business Media. This book was released on 2009-02-19 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: The characterization of combinatorial or geometric structures in terms of their groups of automorphisms has attracted considerable interest in the last decades and is now commonly viewed as a natural generalization of Felix Klein’s Erlangen program(1872).Inaddition,especiallyfor?nitestructures,importantapplications to practical topics such as design theory, coding theory and cryptography have made the ?eld even more attractive. The subject matter of this research monograph is the study and class- cation of ?ag-transitive Steiner designs, that is, combinatorial t-(v,k,1) designs which admit a group of automorphisms acting transitively on incident point-block pairs. As a consequence of the classi?cation of the ?nite simple groups, it has been possible in recent years to characterize Steiner t-designs, mainly for t=2,adm- ting groups of automorphisms with su?ciently strong symmetry properties. For Steiner 2-designs, arguably the most general results have been the classi?cation of all point 2-transitive Steiner 2-designs in 1985 by W. M. Kantor, and the almost complete determination of all ?ag-transitive Steiner 2-designs announced in 1990 byF.Buekenhout,A.Delandtsheer,J.Doyen,P.B.Kleidman,M.W.Liebeck, and J. Saxl. However, despite the classi?cation of the ?nite simple groups, for Steiner t-designs witht> 2 most of the characterizations of these types have remained long-standing challenging problems. Speci?cally, the determination of all ?- transitive Steiner t-designs with 3? t? 6 has been of particular interest and object of research for more than 40 years.

Author : Michael R. Huber
Publisher :
ISBN 13 : 9781282068414
Total Pages : 124 pages
Book Rating : 4.15/5 ( download)

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Download or read book Flag-transitive Steiner Designs written by Michael R. Huber and published by . This book was released on 2009 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: The monograph provides the first full discussion of flag-transitive Steiner designs. This is a central part of the study of highly symmetric combinatorial configurations at the interface of several mathematical disciplines, like finite or incidence geometry, group theory, combinatorics, coding theory, and cryptography. In a sufficiently self-contained and unified manner the classification of all flag-transitive Steiner designs is presented. This recent result settles interesting and challenging questions that have been object of research for more than 40 years. Its proof combines methods from finite group theory, incidence geometry, combinatorics, and number theory. The book contains a broad introduction to the topic, along with many illustrative examples. Moreover, a census of some of the most general results on highly symmetric Steiner designs is given in a survey chapter. The monograph is addressed to graduate students in mathematics and computer science as well as established researchers in design theory, finite or incidence geometry, coding theory, cryptography, algebraic combinatorics, and more generally, discrete mathematics.

Author : Charles J. Colbourn
Publisher : CRC Press
ISBN 13 : 1420010549
Total Pages : 1011 pages
Book Rating : 4.41/5 ( download)

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Download or read book Handbook of Combinatorial Designs written by Charles J. Colbourn and published by CRC Press. This book was released on 2006-11-02 with total page 1011 pages. Available in PDF, EPUB and Kindle. Book excerpt: Continuing in the bestselling, informative tradition of the first edition, the Handbook of Combinatorial Designs, Second Edition remains the only resource to contain all of the most important results and tables in the field of combinatorial design. This handbook covers the constructions, properties, and applications of designs as well as existence

Author : Jacques Calmet
Publisher : Springer Science & Business Media
ISBN 13 : 3540899936
Total Pages : 200 pages
Book Rating : 4.38/5 ( download)

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Download or read book Mathematical Methods in Computer Science written by Jacques Calmet and published by Springer Science & Business Media. This book was released on 2008-12-09 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Festschrift volume contains the proceedings of the conference Mathematical Methods in Computer Science, MMICS 2008, which was held during December 17-19, 2008, in Karlsruhe, Germany, in memory of Thomas Beth. The themes of the conference reflected the many interests of Thomas Beth. Although, these interests might seem diverse, mathematical methods and especially algebra as a language constituted the common denominator of all of his scientific achievements. The 12 contributed talks presented were carefully selected from 30 submissions and cover the topics cryptography, designs, quantum computing, algorithms, and coding theory. Furthermore, this volume contains two invited talks held at the conference. One focuses on the area of coding theory and symbolic computation, an area especially appreciated by Thomas Beth, because it combines algebra and algorithmics. The other one discusses quantum information, which again was a focus of Thomas Beth’s research.

Author : Michael Huber
Publisher : Now Publishers Inc
ISBN 13 : 1601983581
Total Pages : 107 pages
Book Rating : 4.89/5 ( download)

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Download or read book Combinatorial Designs for Authentication and Secrecy Codes written by Michael Huber and published by Now Publishers Inc. This book was released on 2010 with total page 107 pages. Available in PDF, EPUB and Kindle. Book excerpt: Combinatorial Designs for Authentication and Secrecy Codes is a succinct in-depth review and tutorial of a subject that promises to lead to major advances in computer and communication security. This monograph provides a tutorial on combinatorial designs, which gives an overview of the theory. Furthermore, the application of combinatorial designs to authentication and secrecy codes is described in depth. This close relationship of designs with cryptography and information security was first revealed in Shannon's seminal paper on secrecy systems. We bring together in one source foundational and current contributions concerning design-theoretic constructions and characterizations of authentication and secrecy codes.

Author : Isaac Woungang
Publisher : World Scientific
ISBN 13 : 981446919X
Total Pages : 725 pages
Book Rating : 4.97/5 ( download)

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Download or read book Selected Topics In Information And Coding Theory written by Isaac Woungang and published by World Scientific. This book was released on 2010-02-26 with total page 725 pages. Available in PDF, EPUB and Kindle. Book excerpt: The last few years have witnessed rapid advancements in information and coding theory research and applications. This book provides a comprehensive guide to selected topics, both ongoing and emerging, in information and coding theory. Consisting of contributions from well-known and high-profile researchers in their respective specialties, topics that are covered include source coding; channel capacity; linear complexity; code construction, existence and analysis; bounds on codes and designs; space-time coding; LDPC codes; and codes and cryptography.All of the chapters are integrated in a manner that renders the book as a supplementary reference volume or textbook for use in both undergraduate and graduate courses on information and coding theory. As such, it will be a valuable text for students at both undergraduate and graduate levels as well as instructors, researchers, engineers, and practitioners in these fields.Supporting Powerpoint Slides are available upon request for all instructors who adopt this book as a course text.

Author : Thomas Beth
Publisher : Cambridge University Press
ISBN 13 : 9780521444323
Total Pages : 730 pages
Book Rating : 4.22/5 ( download)

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Download or read book Design Theory: Volume 1 written by Thomas Beth and published by Cambridge University Press. This book was released on 1999-11-18 with total page 730 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first volume of the second edition of the standard text on design theory.

Author : Jonathan Spreer
Publisher : Logos Verlag Berlin GmbH
ISBN 13 : 3832529837
Total Pages : 251 pages
Book Rating : 4.33/5 ( download)

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Download or read book Blowups, Slicings and Permutation Groups in Combinatorial Topology written by Jonathan Spreer and published by Logos Verlag Berlin GmbH. This book was released on 2011 with total page 251 pages. Available in PDF, EPUB and Kindle. Book excerpt: Combinatorial topology is a field of research that lies in the intersection of geometric topology, combinatorics, algebraic topology and polytope theory. The main objects of interest are piecewise linear topological manifolds where the manifold is given as a simplicial complex with some additional combinatorial structure. These objects are called combinatorial manifolds. In this work, elements and concepts of algebraic geometry, such as blowups, Morse theory as well as group theory are translated into the field of combinatorial topology in order to establish new tools to study combinatorial manifolds. These tools are applied to triangulated surfaces, 3- and 4-manifolds with and without the help of a computer. Among other things, a new combinatorial triangulation of the K3 surface, combinatorial properties of normal surfaces, and new combinatorial triangulations of pseudomanifolds with multiply transitive automorphism group are presented.

Author : Peter Dembowski
Publisher : Springer Science & Business Media
ISBN 13 : 9783540617860
Total Pages : 414 pages
Book Rating : 4.68/5 ( download)

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Download or read book Finite Geometries written by Peter Dembowski and published by Springer Science & Business Media. This book was released on 1997 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Thomas Beth
Publisher : Cambridge University Press
ISBN 13 : 9780521772310
Total Pages : 524 pages
Book Rating : 4.11/5 ( download)

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Download or read book Design Theory: Volume 2 written by Thomas Beth and published by Cambridge University Press. This book was released on 1999-11-18 with total page 524 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the second edition of the standard text on design theory. Exercises are included throughout, and the book concludes with an extensive and updated bibliography of well over 1800 items.