Download or read book Discrete Mathematics Using Latin Squares written by Charles F. Laywine and published by John Wiley & Sons. This book was released on 1998-09-17 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Latin Squares and Their Applications written by A. Donald Keedwell and published by Elsevier. This book was released on 2015-07-28 with total page 443 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book Latin Squares written by József Dénes and published by Elsevier. This book was released on 1991-01-24 with total page 469 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Orthogonal Latin Squares Based on Groups written by Anthony B. Evans and published by Springer. This book was released on 2018-08-17 with total page 537 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Loops Latin Squares and the Alon taris Conjecture written by Arthur Arnold Drisko and published by . This book was released on 1995 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book I Construction of Three Mutually Orthogonal Latin Squares by the Method of Sum Composition II Geometrical Construction of New Families of Generalized Youden Designs written by Ching-Jung Wu and published by . This book was released on 1976 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book On the Construction of Latin Squares Counterbalanced for Immediate Sequential Effects written by Thomas Rappé Houston and published by . This book was released on 1965 with total page 94 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Theory of Orthomorphisms of Groups and Orthogonal Latin Squares written by A. L. Dulmage and published by . This book was released on 1961 with total page 92 pages. Available in PDF, EPUB and Kindle. Book excerpt: Orthomorphisms are mappings of a finite group onto itself which produce latin squares orthogonal to the square which is the addition table of the group. This paper gives methods of construction of orthomorphisms, their relation to finite plane geometries and their transformation properties. The theory is applied to all groups of order up to and including 12 and to the Veblen Wedderburn projective plane of order 9.
Download or read book On the Completion of Partial Latin Squares written by Tatsuo Oyama and published by . This book was released on 1977 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book On Structure Preserving Groups of Latin Squares and Their Applications to Statistics written by Shin-Sun Chow and published by . This book was released on 1979 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Call of the Primes written by Owen O'Shea and published by Prometheus Books. This book was released on 2016 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: This sampler of entertaining mathematical diversions reveals the elegance and extraordinary usefulness of mathematics for readers who think they have no aptitude for the subject. If you like any kind of game at all, you'll enjoy the amazing mathematical puzzles and patterns presented here in straightforward terms that any layperson can understand. From magic squares and the mysterious qualities of prime numbers to Pythagorean triples, probability theory, the Fibonacci sequence, and more, the author shows that math can be fun while having some profound implications. Such ubiquitous mathematical entities as pi and the Fibonacci numbers are found throughout the natural world and are also the foundation of our technological civilization. By exploring the intriguing games presented here, you'll come away with a greater appreciation for the beauty and importance of these and many more math concepts. This is the perfect book for people who were turned off by math in school but now as adults wonder what they may have missed.
Download or read book Nature written by Sir Norman Lockyer and published by . This book was released on 1902 with total page 1082 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book An Illustration of the Use of the Latin Square in Measuring the Effectiveness of Retail Merchandising Practices written by Bennett A. Dominick and published by . This book was released on 1952 with total page 84 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Distribution free Tests in the Latin Square Design written by Francisco José Pfeilsticker Zimmerman and published by . This book was released on 1983 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Latin square design, its parametric analysis of variance and distribution-free methods; Monte Carlo studies.
Download or read book A Concrete Introduction to Higher Algebra written by Lindsay N. Childs and published by Springer Science & Business Media. This book was released on 2012-12-04 with total page 540 pages. Available in PDF, EPUB and Kindle. Book excerpt: An informal and readable introduction to higher algebra at the post-calculus level. The concepts of ring and field are introduced through study of the familiar examples of the integers and polynomials, with much emphasis placed on congruence classes leading the way to finite groups and finite fields. New examples and theory are integrated in a well-motivated fashion and made relevant by many applications -- to cryptography, coding, integration, history of mathematics, and especially to elementary and computational number theory. The later chapters include expositions of Rabiin's probabilistic primality test, quadratic reciprocity, and the classification of finite fields. Over 900 exercises, ranging from routine examples to extensions of theory, are scattered throughout the book, with hints and answers for many of them included in an appendix.
Download or read book Expansion of a 2 X 2 Latin Square Into a 2 X 2 X 2 Factorial Experiment written by M. K. Barnett and published by . This book was released on 1961 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Cross Over Experiments written by David Ratkowsky and published by CRC Press. This book was released on 2020-01-29 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: Developing a model-based approach that enables any cross-over trial, of any degree of imbalance, to be analyzed both for direct effects and for residual effects, using consistent procedures that employ commercially available statistical software, this text offers a guide to the analysis of cross-over designs.;Illustrating practical applications throughout with examples, this book: emphasizes the importance of choosing highly efficient designs that separate treatment and carryover effects; demonstrates the exact methodology needed to handle the analysis of data; presents a new methodology for the analysis of binary and categorical data; and considers the effects of blocking. The appendices facilitate the choosing of an appropriate design for every experimental need.
