Latin Squares and Their Applications

Latin Squares and Their Applications
Title Latin Squares and Their Applications PDF eBook
Author A. Donald Keedwell
Publisher Elsevier
Pages 443
Release 2015-07-28
Genre Mathematics
ISBN 0444635580

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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

Discrete Mathematics Using Latin Squares

Discrete Mathematics Using Latin Squares
Title Discrete Mathematics Using Latin Squares PDF eBook
Author Charles F. Laywine
Publisher John Wiley & Sons
Pages 336
Release 1998-09-17
Genre Mathematics
ISBN 9780471240648

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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.

Latin Squares

Latin Squares
Title Latin Squares PDF eBook
Author József Dénes
Publisher Elsevier
Pages 469
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.

Orthogonal Latin Squares Based on Groups

Orthogonal Latin Squares Based on Groups
Title Orthogonal Latin Squares Based on Groups PDF eBook
Author Anthony B. Evans
Publisher Springer
Pages 537
Release 2018-08-17
Genre Mathematics
ISBN 3319944304

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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.

Loops, Latin Squares, and the Alon-taris Conjecture

Loops, Latin Squares, and the Alon-taris Conjecture
Title Loops, Latin Squares, and the Alon-taris Conjecture PDF eBook
Author Arthur Arnold Drisko
Publisher
Pages 106
Release 1995
Genre
ISBN

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

I. Construction of Three Mutually Orthogonal Latin Squares by the Method of Sum Composition. II. Geometrical Construction of New Families of Generalized Youden Designs
Title 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 eBook
Author Ching-Jung Wu
Publisher
Pages 150
Release 1976
Genre Magic squares
ISBN

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On the Construction of Latin Squares Counterbalanced for Immediate Sequential Effects

On the Construction of Latin Squares Counterbalanced for Immediate Sequential Effects
Title On the Construction of Latin Squares Counterbalanced for Immediate Sequential Effects PDF eBook
Author Thomas Rappé Houston
Publisher
Pages 94
Release 1965
Genre Magic squares
ISBN

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