Flag Transitive Steiner Designs

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Flag Transitive Steiner Designs

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Author : Michael Huber
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-02-19

Flag Transitive Steiner Designs written by Michael Huber and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-02-19 with Mathematics categories.

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.

Flag Transitive Steiner Designs

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Author : Michael R. Huber
language : en
Publisher:
Release Date : 2009

Flag Transitive Steiner Designs written by Michael R. Huber and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Steiner systems categories.

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.

Handbook Of Combinatorial Designs

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Author : Charles J. Colbourn
language : en
Publisher: CRC Press
Release Date : 2006-11-02

Handbook Of Combinatorial Designs written by Charles J. Colbourn and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-02 with Computers categories.

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

Mathematical Methods In Computer Science

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Author : Jacques Calmet
language : en
Publisher: Springer
Release Date : 2008-12-10

Mathematical Methods In Computer Science written by Jacques Calmet and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-12-10 with Computers categories.

This Festschrift volume contains the proceedings of the conference Mathematical Methods in Computer Science, MMICS 2008, held December 2008, in Karlsruhe, Germany, in memory of Thomas Beth. The themes of the conference reflect his many interests.

Combinatorial Designs For Authentication And Secrecy Codes

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Author : Michael Huber
language : en
Publisher: Now Publishers Inc
Release Date : 2010

Combinatorial Designs For Authentication And Secrecy Codes written by Michael Huber and has been published by Now Publishers Inc this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Computers categories.

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.

Selected Topics In Information And Coding Theory

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Author : Isaac Woungang
language : en
Publisher: World Scientific
Release Date : 2010-02-26

Selected Topics In Information And Coding Theory written by Isaac Woungang and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-02-26 with Computers categories.

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.

Design Theory

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Author : Thomas Beth
language : en
Publisher: Cambridge University Press
Release Date : 1999

Design Theory written by Thomas Beth and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Combinatorial designs and configurations categories.

This is the first volume of the second edition of the standard text on design theory. Since the first edition there has been extensive development of the theory and this book has been thoroughly rewritten and extended during that time. In particular the growing importance of discrete mathematics to many parts of engineering and science have made designs a useful tool for applications. It is suitable for advanced courses and as a reference work, not only for researchers in discrete mathematics or finite algebra, but also for those working in computer and communications engineering and other mathematically oriented disciplines. Exercises are included throughout, and the book concludes with an extensive and updated bibliography of well over 1800 items.

Blowups Slicings And Permutation Groups In Combinatorial Topology

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Author : Jonathan Spreer
language : en
Publisher: Logos Verlag Berlin GmbH
Release Date : 2011

Blowups Slicings And Permutation Groups In Combinatorial Topology written by Jonathan Spreer and has been published by Logos Verlag Berlin GmbH this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Mathematics categories.

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.

Finite Geometries

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Author : Peter Dembowski
language : en
Publisher: Springer Science & Business Media
Release Date : 1968

Finite Geometries written by Peter Dembowski and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1968 with Mathematics categories.

Reihentext + Finite Geometries From the reviews: "Such a vast amount of information as this book contains can only be accomplished in 375 pages by a very economical style of writing... it enables one to have a good look at the forest without being too detracted by the individual trees... The author deserves unstinting praise for the skill, energy, and perseverance which he devoted to this work. The finished product confirms what his many earlier contributions to the subject of finite geometry have already indicated, namely, that he is an undisputed leader in his field." Mathematical Reviews "Finite Geometries" is a very important area of finite mathematics characterized by an interplay of combinatorial, geometric, and algebraic ideas, in which research has been very active and intensive in recent years... makes it clear how large is the field covered by the author in his book. The material is selected most thoroughly, and the author made an effort to collect all that seems to be relevant in finite geometries for the time being... Dembowski's work will be a basic reference book of this field, and it will be considered as a base of the future research... Altogether this is a very well-produced monograph." Publicationes Mathematicae Debrecen 10, tom 16.

Handbook Of Finite Translation Planes

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Author : Norman Johnson
language : en
Publisher: CRC Press
Release Date : 2007-02-15

Handbook Of Finite Translation Planes written by Norman Johnson and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-02-15 with Mathematics categories.

The Handbook of Finite Translation Planes provides a comprehensive listing of all translation planes derived from a fundamental construction technique, an explanation of the classes of translation planes using both descriptions and construction methods, and thorough sketches of the major relevant theorems. From the methods of Andre to coordi