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 Some Aspects Of Latin Squares And Their Applications written by N. Naga Syamala and published by LAP Lambert Academic Publishing. This book was released on 2014-01 with total page 92 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the Present book Chapter - I is an introductory one. It contains the general introduction and statement of the problem of Latin squares. Chapter - II presents the Latin square theory along with the construction of different types of Latin squares. It also gives the description about the layout, analysis and various problems of Latin square design. Chapter - III describes the concept, construction and important application of orthogonal Latin squares. It contains the use of Galois filed in the construction of mutual orthogonal Latin squares. Chapter - IV depicts the various applications of Latin squares in the analysis of design of experiments. It gives the applications of Latin squares, in particular, orthogonal Latin squares in the construction of incomplete block designs such as BIBD, PBIBD., and Latin design. Chapter - V gives the conclusions .study. Some selected references are listed under title 'BIBLIOGRAPHY'.
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 Latin Squares and Their Applications Second Edition written by and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Latin Squares and Their Applications written by József Dénes and published by . This book was released on 1974 with total page 547 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Design and Analysis of Experiments Introduction to Experimental Design written by Klaus Hinkelmann and published by John Wiley & Sons. This book was released on 1994-03-22 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt: Design and analysis of experiments/Hinkelmann.-v.1.
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 Supercomputing written by Vladimir Voevodin and published by Springer. This book was released on 2018-12-31 with total page 701 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 4th Russian Supercomputing Days, RuSCDays 2018, held in Moscow, Russia, in September 2018. The 59 revised full papers and one revised short paper presented were carefully reviewed and selected from 136 submissions. The papers are organized in topical sections on parallel algorithms; supercomputer simulation; high performance architectures, tools and technologies.
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 Elements of Quasigroup Theory and Applications written by Victor Shcherbacov and published by CRC Press. This book was released on 2017-05-12 with total page 423 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to quasigroup theory along with new structural results on some of the quasigroup classes. Many results are presented with some of them from mathematicians of the former USSR. These included results have not been published before in the western mathematical literature. In addition, many of the achievements obtained with regard to applications of quasigroups in coding theory and cryptology are described.
Download or read book The Concise Handbook of Algebra written by Alexander V. Mikhalev and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 629 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is by no means clear what comprises the "heart" or "core" of algebra, the part of algebra which every algebraist should know. Hence we feel that a book on "our heart" might be useful. We have tried to catch this heart in a collection of about 150 short sections, written by leading algebraists in these areas. These sections are organized in 9 chapters A, B, . . . , I. Of course, the selection is partly based on personal preferences, and we ask you for your understanding if some selections do not meet your taste (for unknown reasons, we only had problems in the chapter "Groups" to get enough articles in time). We hope that this book sets up a standard of what all algebraists are supposed to know in "their" chapters; interested people from other areas should be able to get a quick idea about the area. So the target group consists of anyone interested in algebra, from graduate students to established researchers, including those who want to obtain a quick overview or a better understanding of our selected topics. The prerequisites are something like the contents of standard textbooks on higher algebra. This book should also enable the reader to read the "big" Handbook (Hazewinkel 1999-) and other handbooks. In case of multiple authors, the authors are listed alphabetically; so their order has nothing to do with the amounts of their contributions.
Download or read book Latin Squares and Their Applications to Cryptography written by Nathan O. Schmidt and published by . This book was released on 2016 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Combinatorics written by T. P. McDonough and published by Cambridge University Press. This book was released on 1974-11-21 with total page 213 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a record of the papers presented to the fourth British Combinatorial Conference held in Aberystwyth in July 1973. Contributors from all over the world took part and the result is a very useful and up-to-date account of what is happening in the field of combinatorics. A section of problems illustrates some of the topics in need of further investigation.
Download or read book Designs and Graphs written by C.J. Colbourn and published by Elsevier. This book was released on 2016-06-06 with total page 435 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1988, the news of Egmont Köhler's untimely death at the age of 55reached his friends and colleagues. It was widely felt that a lastingmemorial tribute should be organized. The result is the present volume,containing forty-two articles, mostly in combinatorial design theory andgraph theory, and all in memory of Egmont Köhler. Designs and graphswere his areas of particular interest; he will long be remembered for hisresearch on cyclic designs, Skolem sequences, t-designs and theOberwolfach problem. Professors Lenz and Ringel give a detailedappreciation of Köhler's research in the first article of thisvolume. There is, however, one aspect of Egmont Köhler's biographythat merits special attention. Before taking up the study of mathematics atthe age of 31, he had completed training as a musician (studying bothcomposition and violoncello at the Musikhochschule in Berlin), and workedas a cellist in a symphony orchestra for some years. This accounts for hisinterest in the combinatorial aspects of music. His work and lectures inthis direction had begun to attract the interest of many musicians, and hehad commenced work on a book on mathematical aspects of musical theory. Itis tragic indeed that his early death prevented the completion of his work;the surviving paper on the classification and complexity of chordsindicates the loss that his death meant to the area, as he was almostuniquely qualified to bring mathematics and music together, being aprofessional in both fields.
Download or read book Design and Analysis of Experiments Volume 1 written by Klaus Hinkelmann and published by John Wiley & Sons. This book was released on 2007-12-04 with total page 640 pages. Available in PDF, EPUB and Kindle. Book excerpt: This user-friendly new edition reflects a modern and accessible approach to experimental design and analysis Design and Analysis of Experiments, Volume 1, Second Edition provides a general introduction to the philosophy, theory, and practice of designing scientific comparative experiments and also details the intricacies that are often encountered throughout the design and analysis processes. With the addition of extensive numerical examples and expanded treatment of key concepts, this book further addresses the needs of practitioners and successfully provides a solid understanding of the relationship between the quality of experimental design and the validity of conclusions. This Second Edition continues to provide the theoretical basis of the principles of experimental design in conjunction with the statistical framework within which to apply the fundamental concepts. The difference between experimental studies and observational studies is addressed, along with a discussion of the various components of experimental design: the error-control design, the treatment design, and the observation design. A series of error-control designs are presented based on fundamental design principles, such as randomization, local control (blocking), the Latin square principle, the split-unit principle, and the notion of factorial treatment structure. This book also emphasizes the practical aspects of designing and analyzing experiments and features: Increased coverage of the practical aspects of designing and analyzing experiments, complete with the steps needed to plan and construct an experiment A case study that explores the various types of interaction between both treatment and blocking factors, and numerical and graphical techniques are provided to analyze and interpret these interactions Discussion of the important distinctions between two types of blocking factors and their role in the process of drawing statistical inferences from an experiment A new chapter devoted entirely to repeated measures, highlighting its relationship to split-plot and split-block designs Numerical examples using SAS® to illustrate the analyses of data from various designs and to construct factorial designs that relate the results to the theoretical derivations Design and Analysis of Experiments, Volume 1, Second Edition is an ideal textbook for first-year graduate courses in experimental design and also serves as a practical, hands-on reference for statisticians and researchers across a wide array of subject areas, including biological sciences, engineering, medicine, pharmacology, psychology, and business.
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.
Download or read book Latin Squares and Their Applications written by Jozsef Denes and published by . This book was released on 1974 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
