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Combinatorial Design Theory
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Book Synopsis Algorithms in Combinatorial Design Theory by : C.J. Colbourn
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 347 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.
Book Synopsis Combinatorial Design Theory by : C.J. Colbourn
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 483 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.
Book Synopsis Combinatorial Designs by : Douglas Stinson
Download or read book Combinatorial Designs written by Douglas Stinson and published by Springer Science & Business Media. This book was released on 2007-05-08 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: Created to teach students many of the most important techniques used for constructing combinatorial designs, this is an ideal textbook for advanced undergraduate and graduate courses in combinatorial design theory. The text features clear explanations of basic designs, such as Steiner and Kirkman triple systems, mutual orthogonal Latin squares, finite projective and affine planes, and Steiner quadruple systems. In these settings, the student will master various construction techniques, both classic and modern, and will be well-prepared to construct a vast array of combinatorial designs. Design theory offers a progressive approach to the subject, with carefully ordered results. It begins with simple constructions that gradually increase in complexity. Each design has a construction that contains new ideas or that reinforces and builds upon similar ideas previously introduced. A new text/reference covering all apsects of modern combinatorial design theory. Graduates and professionals in computer science, applied mathematics, combinatorics, and applied statistics will find the book an essential resource.
Book Synopsis Design Theory by : Charles C. Lindner
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.
Book Synopsis Combinatorial Designs and their Applications by : Kathleen Quinn
Download or read book Combinatorial Designs and their Applications written by Kathleen Quinn and published by Taylor & Francis. This book was released on 2023-02-06 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: The fruit of a conference that gathered seven very active researchers in the field, Combinatorial Design and their Applications presents a wide but representative range of topics on the non-geometrical aspects of design theory. By concentrating on a few important areas, the authors succeed in providing greater detail in these areas in a more complete and accessible form. Through their contributions to this collection, they help fill a gap in the available combinatorics literature.The papers included in this volume cover recent developments in areas of current interest, such as difference sets, cryptography, and optimal linear codes. Researchers in combinatorics and other areas of pure mathematics, along with researchers in statistics and computer design will find in-depth, up-to-date discussions of design theory and the application of the theory to statistical design, codes, and cryptography.
Book Synopsis Combinatorial Designs for Authentication and Secrecy Codes by : Michael Huber
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.
Book Synopsis Handbook of Combinatorial Designs by : C. J. Colbourn
Download or read book Handbook of Combinatorial Designs written by C. J. Colbourn and published by Chapman and Hall/CRC. This book was released on 2006-11-02 with total page 1016 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 results. Over 30% longer than the first edition, the book builds upon the groundwork of its predecessor while retaining the original contributors' expertise. The first part contains a brief introduction and history of the subject. The following parts focus on four main classes of combinatorial designs: balanced incomplete block designs, orthogonal arrays and Latin squares, pairwise balanced designs, and Hadamard and orthogonal designs. Closely connected to the preceding sections, the next part surveys 65 additional classes of designs, such as balanced ternary, factorial, graphical, Howell, quasi-symmetric, and spherical. The final part presents mathematical and computational background related to design theory. New to the Second Edition An introductory part that provides a general overview and a historical perspective of the area New chapters on the history of design theory, various codes, bent functions, and numerous types of designs Fully updated tables, including BIBDs, MOLS, PBDs, and Hadamard matrices Nearly 2,200 references in a single bibliographic section Meeting the need for up-to-date and accessible tabular and reference information, this handbook provides the tools to understand combinatorial design theory and applications that span the entire discipline. The author maintains a website with more information.
Book Synopsis Designs, Graphs, Codes and their Links by : P. J. Cameron
Download or read book Designs, Graphs, Codes and their Links written by P. J. Cameron and published by Cambridge University Press. This book was released on 1991-09-19 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book stresses the connection between, and the applications of, design theory to graphs and codes. Beginning with a brief introduction to design theory and the necessary background, the book also provides relevant topics for discussion from the theory of graphs and codes.
Book Synopsis Introduction to Combinatorial Designs by : W.D. Wallis
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
Book Synopsis Combinatorial Designs by : W.D. Wallis
Download or read book Combinatorial Designs written by W.D. Wallis and published by CRC Press. This book was released on 1988-04-29 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Algebraic Design Theory by : Warwick De Launey
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.
Book Synopsis Computational and Constructive Design Theory by : W.D. Wallis
Download or read book Computational and Constructive Design Theory written by W.D. Wallis and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the last several years, there has been a significant increase in compu tational combinatorics. The most widely reported results were, of course, the proof of the Four Color Theorem and the proof that there is no projective plane of parameter 10. Although the computer was essential in both proofs, the only reason for this was the fact that life is short. The computations involved were not different in kind from those which have been done by human brains without electronic assistance; they were just longer. Another important fact to notice is that both problems were theoretical, pure mathematical ones. The pursuit of the Four-Color Theorem has led to the development of whole branches of graph theory. The plane of parameter 10 is not an isolated case; its nonexistence is the first (and so far, the only) coun terexample to the conjecture that the Bruck-Chowla-Ryser conditions were necessary and sufficient for the existence of a symmetric balanced incomplete block design; the study of this problem has also led to a number of theoretical advances, including investigation of the relationship between codes and designs.
Book Synopsis Design Theory: Volume 2 by : Thomas Beth
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.
Book Synopsis Combinatorics and Finite Geometry by : Steven T. Dougherty
Download or read book Combinatorics and Finite Geometry written by Steven T. Dougherty and published by Springer Nature. This book was released on 2020-10-30 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: This undergraduate textbook is suitable for introductory classes in combinatorics and related topics. The book covers a wide range of both pure and applied combinatorics, beginning with the very basics of enumeration and then going on to Latin squares, graphs and designs. The latter topic is closely related to finite geometry, which is developed in parallel. Applications to probability theory, algebra, coding theory, cryptology and combinatorial game theory comprise the later chapters. Throughout the book, examples and exercises illustrate the material, and the interrelations between the various topics is emphasized. Readers looking to take first steps toward the study of combinatorics, finite geometry, design theory, coding theory, or cryptology will find this book valuable. Essentially self-contained, there are very few prerequisites aside from some mathematical maturity, and the little algebra required is covered in the text. The book is also a valuable resource for anyone interested in discrete mathematics as it ties together a wide variety of topics.
Book Synopsis Combinatorial Designs and Tournaments by : Ian Anderson (Ph. D.)
Download or read book Combinatorial Designs and Tournaments written by Ian Anderson (Ph. D.) and published by Oxford University Press. This book was released on 1997 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: The mathematics of tournament design are surprisingly subtle, and this book, an extensively revised version of Ellis Horwood's popular Combinatorial Designs: Construction Methods, provides a thorough introduction. It includes a new chapter on league schedules, which discusses round robin tournaments, venue sequences, and carry-over effects. It also discusses balanced tournament designs, double schedules, and bridge and whist tournament design. Readable and authoritative, the book emphasizes throughout the historical development of the material and includes numerous examples and exercises giving detailed constructions.
Book Synopsis Hypergraphs and Designs by : Mario Gionfriddo
Download or read book Hypergraphs and Designs written by Mario Gionfriddo and published by Nova Science Publishers. This book was released on 2015 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Combinatorial designs represent an important area of contemporary discrete mathematics closely related to such fields as finite geometries, regular graphs and multigraphs, factorisations of graphs, linear algebra, number theory, finite fields, group and quasigroup theory, Latin squares, and matroids. It has a history of more than 150 years when it started as a collection of unrelated problems. Nowadays the field is a well-developed theory with deep mathematical results and a wide range of applications in coding theory, cryptography, computer science, and other areas. In the most general setting, a combinatorial design consists of a ground set of elements and a collection of subsets of these elements satisfying some specific restrictions; the latter are often expressed in the language of graphs. On the other side, hypergraph theory is a relatively new field which started in early 60s of the last century as a generalization of graph theory. A hypergraph consists of a ground set of elements and a collection of subsets of these elements without any specific restrictions. In this sense the concept of hypergraph is more general than the concept of combinatorial design. While it started as a generalization of graph theory, hypergraph theory soon became a separate subject because many new properties have been discovered that miss or degenerate in graphs. Compared to graph theory, the language of hypergraphs not only allows us to formulate and solve more general problems, it also helps us to understand and solve several graph theory problems by simplifying and unifying many previously unrelated concepts. The main feature of this book is applying the hypergraph approach to the theory of combinatorial designs. An alternative title of it could be "Combinatorial designs as hypergraphs". There is no analogue to this book on the market. Its primary audience is researchers and graduate students taking courses in design theory, combinatorial geometry, finite geometry, discrete mathematics, graph theory, combinatorics, cryptography, information and coding theory, and similar areas. The aim of this book is to show the connection and mutual benefit between hypergraph theory and design theory. It does not intend to give a survey of all important results or methods in any of these subjects.
Book Synopsis An Introduction to Algebraic and Combinatorial Coding Theory by : Ian F. Blake
Download or read book An Introduction to Algebraic and Combinatorial Coding Theory written by Ian F. Blake and published by Academic Press. This book was released on 2014-05-10 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: An Introduction to Algebraic and Combinatorial Coding Theory focuses on the principles, operations, and approaches involved in the combinatorial coding theory, including linear transformations, chain groups, vector spaces, and combinatorial constructions. The publication first offers information on finite fields and coding theory and combinatorial constructions and coding. Discussions focus on quadratic residues and codes, self-dual and quasicyclic codes, balanced incomplete block designs and codes, polynomial approach to coding, and linear transformations of vector spaces over finite fields. The text then examines coding and combinatorics, including chains and chain groups, equidistant codes, matroids, graphs, and coding, matroids, and dual chain groups. The manuscript also ponders on Möbius inversion formula, Lucas's theorem, and Mathieu groups. The publication is a valuable source of information for mathematicians and researchers interested in the combinatorial coding theory.
