Latin Squares and Their Applications

Latin Squares and Their Applications
Author: A. Donald Keedwell,József Dénes
Publsiher: Elsevier
Total Pages: 443
Release: 2015-07-28
Genre: Mathematics
ISBN: 9780444635587

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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

Latin Squares

Latin Squares
Author: József Dénes,A. Donald Keedwell
Publsiher: Elsevier
Total Pages: 452
Release: 1991-01-24
Genre: Mathematics
ISBN: 0080867863

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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.

Latin Squares and Their Applications

Latin Squares and Their Applications
Author: József Dénes,A. D. Keedwell
Publsiher: Unknown
Total Pages: 547
Release: 1974
Genre: Magic squares
ISBN: 9630502550

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Latin Squares and Their Applications Second Edition

Latin Squares and Their Applications  Second Edition
Author: Anonim
Publsiher: Unknown
Total Pages: 135
Release: 2024
Genre: Electronic Book
ISBN: OCLC:972032143

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Some Aspects Of Latin Squares And Their Applications

Some Aspects Of Latin Squares And Their Applications
Author: N. Naga Syamala,Balasiddamuni Pagadala,D. Chandra Kesavulu Naidu
Publsiher: LAP Lambert Academic Publishing
Total Pages: 92
Release: 2014-01
Genre: Electronic Book
ISBN: 3659504017

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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'.

Discrete Mathematics Using Latin Squares

Discrete Mathematics Using Latin Squares
Author: Charles F. Laywine,Gary L. Mullen
Publsiher: John Wiley & Sons
Total Pages: 336
Release: 1998-09-17
Genre: Mathematics
ISBN: 0471240648

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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.

Orthogonal Latin Squares Based on Groups

Orthogonal Latin Squares Based on Groups
Author: Anthony B. Evans
Publsiher: Springer
Total Pages: 537
Release: 2018-08-17
Genre: Mathematics
ISBN: 9783319944302

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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.

On Structure Preserving Groups of Latin Squares and Their Applications to Statistics

On Structure Preserving Groups of Latin Squares and Their Applications to Statistics
Author: Shin-Sun Chow
Publsiher: Unknown
Total Pages: 134
Release: 1979
Genre: Magic squares
ISBN: MSU:31293100643810

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