Algebraic Design Theory

Author : Warwick De Launey
Publisher : American Mathematical Soc.
ISBN 13 : 0821844962
Total Pages : 314 pages
Book Rating : 4.60/5 ( download)

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Download or read book Algebraic Design Theory written by Warwick De Launey and published by American Mathematical Soc.. This book was released on 2011 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: Combinatorial design theory is a source of simply stated, concrete, yet difficult discrete problems, with the Hadamard conjecture being a prime example. It has become clear that many of these problems are essentially algebraic in nature. This book provides a unified vision of the algebraic themes which have developed so far in design theory. These include the applications in design theory of matrix algebra, the automorphism group and its regular subgroups, the composition of smaller designs to make larger designs, and the connection between designs with regular group actions and solutions to group ring equations. Everything is explained at an elementary level in terms of orthogonality sets and pairwise combinatorial designs--new and simple combinatorial notions which cover many of the commonly studied designs. Particular attention is paid to how the main themes apply in the important new context of cocyclic development. Indeed, this book contains a comprehensive account of cocyclic Hadamard matrices. The book was written to inspire researchers, ranging from the expert to the beginning student, in algebra or design theory, to investigate the fundamental algebraic problems posed by combinatorial design theory.

Author : Charles J. Colbourn
Publisher : Springer
ISBN 13 : 331917729X
Total Pages : 261 pages
Book Rating : 4.98/5 ( download)

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Download or read book Algebraic Design Theory and Hadamard Matrices written by Charles J. Colbourn and published by Springer. This book was released on 2015-09-03 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume develops the depth and breadth of the mathematics underlying the construction and analysis of Hadamard matrices, and their use in the construction of combinatorial designs. At the same time, it pursues current research in their numerous applications in security and cryptography, quantum information, and communications. Bridges among diverse mathematical threads and extensive applications make this an invaluable source for understanding both the current state of the art and future directions.​ ​The existence of Hadamard matrices remains one of the most challenging open questions in combinatorics. Substantial progress on their existence has resulted from advances in algebraic design theory using deep connections with linear algebra, abstract algebra, finite geometry, number theory, and combinatorics. Hadamard matrices arise in a very diverse set of applications. Starting with applications in experimental design theory and the theory of error-correcting codes, they have found unexpected and important applications in cryptography, quantum information theory, communications, and networking.

Author : C.J. Colbourn
Publisher : Elsevier
ISBN 13 : 9780080872605
Total Pages : 469 pages
Book Rating : 4.03/5 ( download)

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Download or read book Combinatorial Design Theory written by C.J. Colbourn and published by Elsevier. This book was released on 2011-09-22 with total page 469 pages. Available in PDF, EPUB and Kindle. Book excerpt: Combinatorial design theory is a vibrant area of combinatorics, connecting graph theory, number theory, geometry, and algebra with applications in experimental design, coding theory, and numerous applications in computer science. This volume is a collection of forty-one state-of-the-art research articles spanning all of combinatorial design theory. The articles develop new methods for the construction and analysis of designs and related combinatorial configurations; both new theoretical methods, and new computational tools and results, are presented. In particular, they extend the current state of knowledge on Steiner systems, Latin squares, one-factorizations, block designs, graph designs, packings and coverings, and develop recursive and direct constructions. The contributions form an overview of the current diversity of themes in design theory for those peripherally interested, while researchers in the field will find it to be a major collection of research advances. The volume is dedicated to Alex Rosa, who has played a major role in fostering and developing combinatorial design theory.

Author : Charles C. Lindner
Publisher : CRC Press
ISBN 13 : 1420082973
Total Pages : 272 pages
Book Rating : 4.75/5 ( download)

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Download or read book Design Theory written by Charles C. Lindner and published by CRC Press. This book was released on 2017-03-27 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: Design Theory, Second Edition presents some of the most important techniques used for constructing combinatorial designs. It augments the descriptions of the constructions with many figures to help students understand and enjoy this branch of mathematics. This edition now offers a thorough development of the embedding of Latin squares and combinatorial designs. It also presents some pure mathematical ideas, including connections between universal algebra and graph designs. The authors focus on several basic designs, including Steiner triple systems, Latin squares, and finite projective and affine planes. They produce these designs using flexible constructions and then add interesting properties that may be required, such as resolvability, embeddings, and orthogonality. The authors also construct more complicated structures, such as Steiner quadruple systems. By providing both classical and state-of-the-art construction techniques, this book enables students to produce many other types of designs.

Author : D. Braha
Publisher : Springer Science & Business Media
ISBN 13 : 1475728727
Total Pages : 684 pages
Book Rating : 4.29/5 ( download)

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Download or read book A Mathematical Theory of Design: Foundations, Algorithms and Applications written by D. Braha and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 684 pages. Available in PDF, EPUB and Kindle. Book excerpt: Formal Design Theory (PDT) is a mathematical theory of design. The main goal of PDT is to develop a domain independent core model of the design process. The book focuses the reader's attention on the process by which ideas originate and are developed into workable products. In developing PDT, we have been striving toward what has been expressed by the distinguished scholar Simon (1969): that "the science of design is possible and some day we will be able to talk in terms of well-established theories and practices. " The book is divided into five interrelated parts. The conceptual approach is presented first (Part I); followed by the theoretical foundations of PDT (Part II), and from which the algorithmic and pragmatic implications are deduced (Part III). Finally, detailed case-studies illustrate the theory and the methods of the design process (Part IV), and additional practical considerations are evaluated (Part V). The generic nature of the concepts, theory and methods are validated by examples from a variety of disciplines. FDT explores issues such as: algebraic representation of design artifacts, idealized design process cycle, and computational analysis and measurement of design process complexity and quality. FDT's axioms convey the assumptions of the theory about the nature of artifacts, and potential modifications of the artifacts in achieving desired goals or functionality. By being able to state these axioms explicitly, it is possible to derive theorems and corollaries, as well as to develop specific analytical and constructive methodologies.

Author : W.D. Wallis
Publisher : CRC Press
ISBN 13 : 1584888393
Total Pages : 324 pages
Book Rating : 4.90/5 ( download)

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Download or read book Introduction to Combinatorial Designs written by W.D. Wallis and published by CRC Press. This book was released on 2016-04-19 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: Combinatorial theory is one of the fastest growing areas of modern mathematics. Focusing on a major part of this subject, Introduction to Combinatorial Designs, Second Edition provides a solid foundation in the classical areas of design theory as well as in more contemporary designs based on applications in a variety of fields. After an o

Author : Jeffrey H. Dinitz
Publisher : John Wiley & Sons
ISBN 13 : 9780471531418
Total Pages : 660 pages
Book Rating : 4.13/5 ( download)

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Download or read book Contemporary Design Theory written by Jeffrey H. Dinitz and published by John Wiley & Sons. This book was released on 1992-08-04 with total page 660 pages. Available in PDF, EPUB and Kindle. Book excerpt: Foremost experts in their field have contributed articles resulting in a compilation of useful and timely surveys in this ever-expanding field. Each of these 12 original papers covers important aspects of design theory including several in areas that have not previously been surveyed. Also contains surveys updating earlier ones where research is particularly active.

Author : Thomas Beth
Publisher : Cambridge University Press
ISBN 13 : 9780521333344
Total Pages : 688 pages
Book Rating : 4.42/5 ( download)

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Download or read book Design Theory written by Thomas Beth and published by Cambridge University Press. This book was released on 1987-03-05 with total page 688 pages. Available in PDF, EPUB and Kindle. Book excerpt: Now released in a special low-priced edition, this comprehensive treatment of the theory of combinatorial designs will be welcomed by all mathematicians working in combinatorics. The reader is expected to be familiar with basic algebra, but other than that, the work is self-contained, so is well-suited for advanced courses or as a reference: exercises are included throughout. The book ends with a comprehensive and thorough bibliography of over 500 items.

Author : C.J. Colbourn
Publisher : Elsevier
ISBN 13 : 9780080872254
Total Pages : 333 pages
Book Rating : 4.55/5 ( download)

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Download or read book Algorithms in Combinatorial Design Theory written by C.J. Colbourn and published by Elsevier. This book was released on 1985-01-01 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: The scope of the volume includes all algorithmic and computational aspects of research on combinatorial designs. Algorithmic aspects include generation, isomorphism and analysis techniques - both heuristic methods used in practice, and the computational complexity of these operations. The scope within design theory includes all aspects of block designs, Latin squares and their variants, pairwise balanced designs and projective planes and related geometries.

Author : D. R. Hughes
Publisher : Cambridge University Press
ISBN 13 : 9780521358729
Total Pages : 252 pages
Book Rating : 4.28/5 ( download)

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Download or read book Design Theory written by D. R. Hughes and published by Cambridge University Press. This book was released on 1988-03-10 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: Design theory has grown to be a subject of considerable interest in mathematics, not only in itself, but for its connections to other fields such as geometry, group theory, graph theory and coding theory. This textbook, first published in 1985, is intended to be an accessible introduction to the subject for advanced undergraduate and beginning graduate students which should prepare them for research in design theory and its applications. The first four chapters of the book are designed to be the core of any course in the subject, while the remaining chapters can be utilized in more advanced or longer courses. The authors assume some knowledge of linear algebra for the first half of the book, but for the second half, students need further background in algebra.