I. Construction of Three Mutually Orthogonal Latin Squares by the Method of Sum Composition. II. Geometrical Construction of New Families of Generalized Youden Designs PDF Download

Author: Ching-Jung Wu
Publisher:
ISBN:
Category : Magic squares
Languages : en
Pages : 150

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Author: József Dénes
Publisher: Elsevier
ISBN: 9780080867861
Category : Mathematics
Languages : en
Pages : 452

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Book Description
In 1974 the editors of the present volume published a well-received book entitled ``Latin Squares and their Applications''. It included a list of 73 unsolved problems of which about 20 have been completely solved in the intervening period and about 10 more have been partially solved. The present work comprises six contributed chapters and also six further chapters written by the editors themselves. As well as discussing the advances which have been made in the subject matter of most of the chapters of the earlier book, this new book contains one chapter which deals with a subject (r-orthogonal latin squares) which did not exist when the earlier book was written. The success of the former book is shown by the two or three hundred published papers which deal with questions raised by it.

Author: Charles F. Laywine
Publisher: John Wiley & Sons
ISBN: 9780471240648
Category : Mathematics
Languages : en
Pages : 336

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Book Description
Over the past two decades, research in the theory of Latin Squares has been growing at a fast pace, and new significant developments have taken place. This book offers a unique approach to various areas of discrete mathematics through the use of Latin Squares.

Author: Anthony B. Evans
Publisher:
ISBN: 9783319944319
Category : Magic squares
Languages : en
Pages : 537

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Book Description
This monograph presents a unified exposition of latin squares and mutually orthogonal sets of latin squares based on groups. Its focus is on orthomorphisms and complete mappings of finite groups, while also offering a complete proof of the Hall-Paige conjecture. The use of latin squares in constructions of nets, affine planes, projective planes, and transversal designs also motivates this inquiry. The text begins by introducing fundamental concepts, like the tests for determining whether a latin square is based on a group, as well as orthomorphisms and complete mappings. From there, it describes the existence problem for complete mappings of groups, building up to the proof of the Hall-Paige conjecture. The third part presents a comprehensive study of orthomorphism graphs of groups, while the last part provides a discussion of Cartesian projective planes, related combinatorial structures, and a list of open problems. Expanding the author's 1992 monograph, Orthomorphism Graphs of Groups, this book is an essential reference tool for mathematics researchers or graduate students tackling latin square problems in combinatorics. Its presentation draws on a basic understanding of finite group theory, finite field theory, linear algebra, and elementary number theory--more advanced theories are introduced in the text as needed.--

Author: D.R. Cox
Publisher: CRC Press
ISBN: 1420035835
Category : Mathematics
Languages : en
Pages : 337

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Why study the theory of experiment design? Although it can be useful to know about special designs for specific purposes, experience suggests that a particular design can rarely be used directly. It needs adaptation to accommodate the circumstances of the experiment. Successful designs depend upon adapting general theoretical principles to the spec

Author: A. Donald Keedwell
Publisher: Elsevier
ISBN: 0444635580
Category : Mathematics
Languages : en
Pages : 443

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Book Description
Latin Squares and Their Applications, Second edition offers a long-awaited update and reissue of this seminal account of the subject. The revision retains foundational, original material from the frequently-cited 1974 volume but is completely updated throughout. As with the earlier version, the author hopes to take the reader ‘from the beginnings of the subject to the frontiers of research’. By omitting a few topics which are no longer of current interest, the book expands upon active and emerging areas. Also, the present state of knowledge regarding the 73 then-unsolved problems given at the end of the first edition is discussed and commented upon. In addition, a number of new unsolved problems are proposed. Using an engaging narrative style, this book provides thorough coverage of most parts of the subject, one of the oldest of all discrete mathematical structures and still one of the most relevant. However, in consequence of the huge expansion of the subject in the past 40 years, some topics have had to be omitted in order to keep the book of a reasonable length. Latin squares, or sets of mutually orthogonal latin squares (MOLS), encode the incidence structure of finite geometries; they prescribe the order in which to apply the different treatments in designing an experiment in order to permit effective statistical analysis of the results; they produce optimal density error-correcting codes; they encapsulate the structure of finite groups and of more general algebraic objects known as quasigroups. As regards more recreational aspects of the subject, latin squares provide the most effective and efficient designs for many kinds of games tournaments and they are the templates for Sudoku puzzles. Also, they provide a number of ways of constructing magic squares, both simple magic squares and also ones with additional properties. Retains the organization and updated foundational material from the original edition Explores current and emerging research topics Includes the original 73 ‘Unsolved Problems’ with the current state of knowledge regarding them, as well as new Unsolved Problems for further study

Author: Gary W. Oehlert
Publisher: W. H. Freeman
ISBN: 9780716735106
Category : Mathematics
Languages : en
Pages : 600

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Book Description
Oehlert's text is suitable for either a service course for non-statistics graduate students or for statistics majors. Unlike most texts for the one-term grad/upper level course on experimental design, Oehlert's new book offers a superb balance of both analysis and design, presenting three practical themes to students: • when to use various designs • how to analyze the results • how to recognize various design options Also, unlike other older texts, the book is fully oriented toward the use of statistical software in analyzing experiments.

Author: Neil H. Timm
Publisher: Springer Science & Business Media
ISBN: 0387227717
Category : Mathematics
Languages : en
Pages : 709

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Book Description
This book provides a broad overview of the basic theory and methods of applied multivariate analysis. The presentation integrates both theory and practice including both the analysis of formal linear multivariate models and exploratory data analysis techniques. Each chapter contains the development of basic theoretical results with numerous applications illustrated using examples from the social and behavioral sciences, and other disciplines. All examples are analyzed using SAS for Windows Version 8.0.

Author: Peter W. M. John
Publisher: SIAM
ISBN: 0898714273
Category : Mathematics
Languages : en
Pages : 378

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Book Description
An invaluable reference on the design of experiments. Includes hard-to-find information on change-over designs and analysis of covariance.

Author: Paul D. Berger
Publisher: Springer
ISBN: 3319645838
Category : Mathematics
Languages : en
Pages : 639

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Book Description
This text introduces and provides instruction on the design and analysis of experiments for a broad audience. Formed by decades of teaching, consulting, and industrial experience in the Design of Experiments field, this new edition contains updated examples, exercises, and situations covering the science and engineering practice. This text minimizes the amount of mathematical detail, while still doing full justice to the mathematical rigor of the presentation and the precision of statements, making the text accessible for those who have little experience with design of experiments and who need some practical advice on using such designs to solve day-to-day problems. Additionally, an intuitive understanding of the principles is always emphasized, with helpful hints throughout.