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Latin Squares And Their Applications
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Book Synopsis Latin Squares and Their Applications by : A. Donald Keedwell
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.
Book Synopsis Latin Squares and Their Applications by : József Dénes
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:
Book Synopsis Latin Squares and Their Applications (Second Edition) by :
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:
Book Synopsis Discrete Mathematics Using Latin Squares by : Charles F. Laywine
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.
Book Synopsis Some Aspects Of Latin Squares And Their Applications by : N. Naga Syamala
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'.
Book Synopsis Latin Squares and Their Applications by : Jozsef Denes
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:
Book Synopsis From Great Discoveries in Number Theory to Applications by : Michal Křížek
Download or read book From Great Discoveries in Number Theory to Applications written by Michal Křížek and published by Springer Nature. This book was released on 2021-09-21 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an overview of many interesting properties of natural numbers, demonstrating their applications in areas such as cryptography, geometry, astronomy, mechanics, computer science, and recreational mathematics. In particular, it presents the main ideas of error-detecting and error-correcting codes, digital signatures, hashing functions, generators of pseudorandom numbers, and the RSA method based on large prime numbers. A diverse array of topics is covered, from the properties and applications of prime numbers, some surprising connections between number theory and graph theory, pseudoprimes, Fibonacci and Lucas numbers, and the construction of Magic and Latin squares, to the mathematics behind Prague’s astronomical clock. Introducing a general mathematical audience to some of the basic ideas and algebraic methods connected with various types of natural numbers, the book will provide invaluable reading for amateurs and professionals alike.
Book Synopsis Orthogonal Latin Squares Based on Groups by : Anthony B. Evans
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.
Book Synopsis On Structure Preserving Groups of Latin Squares and Their Applications to Statistics by : Shin-Sun Chow
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:
Book Synopsis Combinatorial Methods with Computer Applications by : Jonathan L. Gross
Download or read book Combinatorial Methods with Computer Applications written by Jonathan L. Gross and published by CRC Press. This book was released on 2016-04-19 with total page 664 pages. Available in PDF, EPUB and Kindle. Book excerpt: Combinatorial Methods with Computer Applications provides in-depth coverage of recurrences, generating functions, partitions, and permutations, along with some of the most interesting graph and network topics, design constructions, and finite geometries. Requiring only a foundation in discrete mathematics, it can serve as the textbook in a combinat
Download or read book Orthogonal Arrays written by A.S. Hedayat and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: Orthogonal arrays have played a vital role in improving the quality of products manufactured throughout the world. This first book on the subject since its introduction more than fifty years ago serves as a key resource to this area of designing experiments. Most of the arrays obtained by the methods in this book are available electronically. Anyone running experiments - whether in a chemistry lab or a manufacturing plant, or in agricultural or medical research - will find this book useful.
Book Synopsis Mutually Nearly Orthogonal Latin Squares and Their Applications by : Elise B. Pasles
Download or read book Mutually Nearly Orthogonal Latin Squares and Their Applications written by Elise B. Pasles and published by . This book was released on 2004 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Latin Squares and Their Applications to Cryptography by : Nathan O. Schmidt
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:
Book Synopsis Introduction to Combinatorics by : Walter D. Wallis
Download or read book Introduction to Combinatorics written by Walter D. Wallis and published by CRC Press. This book was released on 2016-12-12 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: What Is Combinatorics Anyway? Broadly speaking, combinatorics is the branch of mathematics dealing with different ways of selecting objects from a set or arranging objects. It tries to answer two major kinds of questions, namely, counting questions: how many ways can a selection or arrangement be chosen with a particular set of properties; and structural questions: does there exist a selection or arrangement of objects with a particular set of properties? The authors have presented a text for students at all levels of preparation. For some, this will be the first course where the students see several real proofs. Others will have a good background in linear algebra, will have completed the calculus stream, and will have started abstract algebra. The text starts by briefly discussing several examples of typical combinatorial problems to give the reader a better idea of what the subject covers. The next chapters explore enumerative ideas and also probability. It then moves on to enumerative functions and the relations between them, and generating functions and recurrences., Important families of functions, or numbers and then theorems are presented. Brief introductions to computer algebra and group theory come next. Structures of particular interest in combinatorics: posets, graphs, codes, Latin squares, and experimental designs follow. The authors conclude with further discussion of the interaction between linear algebra and combinatorics. Features Two new chapters on probability and posets. Numerous new illustrations, exercises, and problems. More examples on current technology use A thorough focus on accuracy Three appendices: sets, induction and proof techniques, vectors and matrices, and biographies with historical notes, Flexible use of MapleTM and MathematicaTM
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 CRC Handbook of Combinatorial Designs by : Charles J. Colbourn
Download or read book CRC Handbook of Combinatorial Designs written by Charles J. Colbourn and published by CRC Press. This book was released on 2010-12-12 with total page 778 pages. Available in PDF, EPUB and Kindle. Book excerpt: From experimental design to cryptography, this comprehensive, easy-to-access reference contains literally all the facts you need on combinatorial designs. It includes constructions of designs, existence results, and properties of designs. Organized into six main parts, the CRC Handbook of Combinatorial Designs covers:
