Combinatorial Theory and Statistical Design
Combinatorial Theory and Statistical Design

Author: Gregory M. Constantine

Publisher:

Published: 1987-05-04

Total Pages: 494

ISBN-13:

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This balanced and comprehensive treatment of topics in discrete mathematics and statistical design raises new questions and assesses potential difficulties surrounding various techniques. Covers a broad range of topics, from counting and enumeration techniques to graphs and networks, combinatorial and statistical designs, and partially ordered sets. Presents several methods of construction, many appearing for the first time in book form. Theory is carefully developed and presented in a conversational way that gears readers toward important new ideas and illustrates the necessity of introducing new techniques. Also examines the practical applications of results. Two entire sections are devoted to Polya's and DeBruign's enumeration of results, presenting them in the form of step-by-step recipes, ready for use by research workers.

Combinatorial Designs and their Applications
Combinatorial Designs and their Applications

Author: Kathleen Quinn

Publisher: Taylor & Francis

Published: 2023-02-06

Total Pages: 160

ISBN-13: 1351459740

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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.

Introduction to Combinatorial Designs
Introduction to Combinatorial Designs

Author: W.D. Wallis

Publisher: CRC Press

Published: 2016-04-19

Total Pages: 324

ISBN-13: 1584888393

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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

Algorithms in Combinatorial Design Theory
Algorithms in Combinatorial Design Theory

Author: C.J. Colbourn

Publisher: Elsevier

Published: 1985-01-01

Total Pages: 347

ISBN-13: 0080872255

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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.

Introduction to Combinatorial Theory
Introduction to Combinatorial Theory

Author: R. C. Bose

Publisher:

Published: 1984-03-19

Total Pages: 270

ISBN-13:

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A ``hands-on'' constructive and computational approach to combinatorial topics with real-life modern applications. Provides a simple treatment of the subject. Introduces topics such as counting, designs and graphs. The notation is standard and kept to a minimum. Chapters end with historical remarks and suggestions for further reading.

A Survey of Combinatorial Theory
A Survey of Combinatorial Theory

Author: Jagdish N. Srivastava

Publisher: Elsevier

Published: 2014-05-12

Total Pages: 476

ISBN-13: 1483278174

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A Survey of Combinatorial Theory covers the papers presented at the International Symposium on Combinatorial Mathematics and its Applications, held at Colorado State University (CSU), Fort Collins, Colorado on September 9-11, 1971. The book focuses on the principles, operations, and approaches involved in combinatorial theory, including the Bose-Nelson sorting problem, Golay code, and Galois geometries. The selection first ponders on classical and modern topics in finite geometrical structures; balanced hypergraphs and applications to graph theory; and strongly regular graph derived from the perfect ternary Golay code. Discussions focus on perfect ternary Golay code, finite projective and affine planes, Galois geometries, and other geometric structures. The book then examines the characterization problems of combinatorial graph theory, line-minimal graphs with cyclic group, circle geometry in higher dimensions, and Cayley diagrams and regular complex polygons. The text discusses combinatorial problems in finite Abelian groups, dissection graphs of planar point sets, combinatorial problems and results in fractional replication, Bose-Nelson sorting problem, and some combinatorial aspects of coding theory. The text also reviews the enumerative theory of planar maps, balanced arrays and orthogonal arrays, existence of resolvable block designs, and combinatorial problems in communication networks. The selection is a valuable source of information for mathematicians and researchers interested in the combinatorial theory.

Combinatorial Design Theory
Combinatorial Design Theory

Author: C.J. Colbourn

Publisher: Elsevier

Published: 2011-09-22

Total Pages: 483

ISBN-13: 0080872603

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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.

Combinatorial Designs
Combinatorial Designs

Author: Douglas Stinson

Publisher: Springer Science & Business Media

Published: 2007-05-08

Total Pages: 306

ISBN-13: 0387217371

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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.

Combinatorics of Experimental Design
Combinatorics of Experimental Design

Author: Anne Penfold Street

Publisher: Oxford University Press, USA

Published: 1987

Total Pages: 400

ISBN-13: 9780198532552

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This book describes direct and recursive methods for the construction of combinatorial designs. It is ideally suited to the statistician through its discussion of how the designs currently used in experimental work have been obtained and through its coverage of other known and potentially useful designs. It is equally suited to the needs of the combinatorialist, with its stress on the statistical motivation for studying particular finite structures and its suggestions of open problems in the construction of new designs with useful properties for the experimentalist. Designs are discussed within a unified framework, showing the interplay between elegant structure and practical use.

Combinatorial Theory
Combinatorial Theory

Author: Marshall Hall

Publisher: John Wiley & Sons

Published: 2011-08-15

Total Pages: 462

ISBN-13: 1118031113

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Includes proof of van der Waerden's 1926 conjecture on permanents, Wilson's theorem on asymptotic existence, and other developments in combinatorics since 1967. Also covers coding theory and its important connection with designs, problems of enumeration, and partition. Presents fundamentals in addition to latest advances, with illustrative problems at the end of each chapter. Enlarged appendixes include a longer list of block designs.