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Latin Squares and Their Applications

Latin Squares and Their Applications
A Book

by A. Donald Keedwell,József Dénes

  • Publisher : Elsevier
  • Release : 2015-07-28
  • Pages : 455
  • ISBN : 0444635580
  • Language : En, Es, Fr & De
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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 and Their Applications

Latin Squares and Their Applications
A Book

by József Dénes,A. D. Keedwell

  • Publisher : Unknown Publisher
  • Release : 1974
  • Pages : 547
  • ISBN : 9780340124895
  • Language : En, Es, Fr & De
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Latin Squares

Latin Squares
New Developments in the Theory and Applications

by József Dénes,A. Donald Keedwell

  • Publisher : Elsevier
  • Release : 1991-01-24
  • Pages : 452
  • ISBN : 9780080867861
  • Language : En, Es, Fr & De
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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
A Book

by J. Denes

  • Publisher : Unknown Publisher
  • Release : 1974
  • Pages : 547
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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Some Aspects Of Latin Squares And Their Applications

Some Aspects Of Latin Squares And Their Applications
On Latin Square Theory

by N. Naga Syamala,Balasiddamuni Pagadala,D. Chandra Kesavulu Naidu

  • Publisher : LAP Lambert Academic Publishing
  • Release : 2014-01
  • Pages : 92
  • ISBN : 9783659504013
  • Language : En, Es, Fr & De
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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'.

Latin Squares and Their Applications (Second Edition)

Latin Squares and Their Applications (Second Edition)
A Book

by Anonim

  • Publisher : Unknown Publisher
  • Release : 2021
  • Pages : 129
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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On Structure Preserving Groups of Latin Squares and Their Applications to Statistics

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

by Shin-Sun Chow

  • Publisher : Unknown Publisher
  • Release : 1979
  • Pages : 112
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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Mutually Nearly Orthogonal Latin Squares and Their Applications

Mutually Nearly Orthogonal Latin Squares and Their Applications
A Book

by Elise B. Pasles

  • Publisher : Unknown Publisher
  • Release : 2004
  • Pages : 188
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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Latin Squares and Their Applications to Cryptography

Latin Squares and Their Applications to Cryptography
A Book

by Nathan O. Schmidt

  • Publisher : Unknown Publisher
  • Release : 2016
  • Pages : 210
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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Latin Squares and Their Applications

Latin Squares and Their Applications
A Book

by József Dénes (mathématicien).),A. D.. Keedwell

  • Publisher : Unknown Publisher
  • Release : 1974
  • Pages : 547
  • ISBN : 9780122093500
  • Language : En, Es, Fr & De
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Orthogonal Latin Squares Based on Groups

Orthogonal Latin Squares Based on Groups
A Book

by Anthony B. Evans

  • Publisher : Springer
  • Release : 2018-08-17
  • Pages : 537
  • ISBN : 3319944304
  • Language : En, Es, Fr & De
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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.

Discrete Mathematics Using Latin Squares

Discrete Mathematics Using Latin Squares
A Book

by Charles F. Laywine,Gary L. Mullen

  • Publisher : John Wiley & Sons
  • Release : 1998-09-17
  • Pages : 305
  • ISBN : 9780471240648
  • Language : En, Es, Fr & De
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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 Square Design and Their Applications

Latin Square Design and Their Applications
Concepts in Design of Experiments

by G. Mokesh Rayalu,J. Ravi Sankar,A. Felix

  • Publisher : Unknown Publisher
  • Release : 2016-12-10
  • Pages : 72
  • ISBN : 9783659844263
  • Language : En, Es, Fr & De
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Combinatorial Designs and their Applications

Combinatorial Designs and their Applications
A Book

by Kathleen Quinn,Bridget Webb,Chris Rowley,F C Holroyd

  • Publisher : CRC Press
  • Release : 1999-01-29
  • Pages : 160
  • ISBN : 9780849306594
  • Language : En, Es, Fr & De
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The fruit of a conference that gathered seven very active researchers in the field, Combinatorial Design and their Applications presents a wide but representative range of topics on the non-geometrical aspects of design theory. By concentrating on a few important areas, the authors succeed in providing greater detail in these areas in a more complete and accessible form. Through their contributions to this collection, they help fill a gap in the available combinatorics literature. The papers included in this volume cover recent developments in areas of current interest, such as difference sets, cryptography, and optimal linear codes. Researchers in combinatorics and other areas of pure mathematics, along with researchers in statistics and computer design will find in-depth, up-to-date discussions of design theory and the application of the theory to statistical design, codes, and cryptography.

Bipartite Graphs and Their Applications

Bipartite Graphs and Their Applications
A Book

by Armen S. Asratian,Tristan M. J. Denley,Roland Häggkvist

  • Publisher : Cambridge University Press
  • Release : 1998-07-13
  • Pages : 259
  • ISBN : 9780521593458
  • Language : En, Es, Fr & De
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This book treats the fundamental mathematical properties that hold for a family of Gaussian random variables.

Encyclopaedia of Mathematics

Encyclopaedia of Mathematics
Orbit - Rayleigh Equation

by Michiel Hazewinkel

  • Publisher : Springer Science & Business Media
  • Release : 2012-12-06
  • Pages : 506
  • ISBN : 940151237X
  • Language : En, Es, Fr & De
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This ENCYCLOPAEDIA OF MA THEMA TICS aims to be a reference work for all parts of mathe matics. It is a translation with updates and editorial comments of the Soviet Mathematical Encyclopaedia published by 'Soviet Encyclopaedia Publishing House' in five volumes in 1977-1985. The annotated translation consists of ten volumes including a special index volume. There are three kinds of articles in this ENCYCLOPAEDIA. First of all there are survey-type articles dealing with the various main directions in mathematics (where a rather fine subdivi sion has been used). The main requirement for these articles has been that they should give a reasonably complete up-to-date account of the current state of affairs in these areas and that they should be maximally accessible. On the whole, these articles should be understandable to mathematics students in their first specialization years, to graduates from other mathematical areas and, depending on the specific subject, to specialists in other domains of science, en gineers and teachers of mathematics. These articles treat their material at a fairly general level and aim to give an idea of the kind of problems, techniques and concepts involved in the area in question. They also contain background and motivation rather than precise statements of precise theorems with detailed definitions and technical details on how to carry out proofs and constructions. The second kind of article, of medium length, contains more detailed concrete problems, results and techniques.

Encyclopaedia of Mathematics

Encyclopaedia of Mathematics
Monge — Ampère Equation — Rings and Algebras

by M. Hazewinkel

  • Publisher : Springer
  • Release : 2013-12-01
  • Pages : 929
  • ISBN : 1489937919
  • Language : En, Es, Fr & De
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The Zen of Magic Squares, Circles, and Stars

The Zen of Magic Squares, Circles, and Stars
An Exhibition of Surprising Structures Across Dimensions

by Clifford A. Pickover

  • Publisher : Princeton University Press
  • Release : 2003
  • Pages : 413
  • ISBN : 0691115974
  • Language : En, Es, Fr & De
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Provides a history of magic squares and similar structures, describing their construction and classification, along with informaiton on newly discovered objects.

The Zen Of Magic Squares,Circles And Stars

The Zen Of Magic Squares,Circles And Stars
A Book

by M K Joseph

  • Publisher : Universities Press
  • Release : 2021
  • Pages : 129
  • ISBN : 9788173714665
  • Language : En, Es, Fr & De
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Designs and Graphs

Designs and Graphs
A Book

by C.J. Colbourn,D. Jungnickel,A. Rosa

  • Publisher : Elsevier
  • Release : 2016-06-06
  • Pages : 129
  • ISBN : 1483294757
  • Language : En, Es, Fr & De
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In 1988, the news of Egmont Köhler's untimely death at the age of 55 reached his friends and colleagues. It was widely felt that a lasting memorial tribute should be organized. The result is the present volume, containing forty-two articles, mostly in combinatorial design theory and graph theory, and all in memory of Egmont Köhler. Designs and graphs were his areas of particular interest; he will long be remembered for his research on cyclic designs, Skolem sequences, t-designs and the Oberwolfach problem. Professors Lenz and Ringel give a detailed appreciation of Köhler's research in the first article of this volume. There is, however, one aspect of Egmont Köhler's biography that merits special attention. Before taking up the study of mathematics at the age of 31, he had completed training as a musician (studying both composition and violoncello at the Musikhochschule in Berlin), and worked as a cellist in a symphony orchestra for some years. This accounts for his interest in the combinatorial aspects of music. His work and lectures in this direction had begun to attract the interest of many musicians, and he had commenced work on a book on mathematical aspects of musical theory. It is tragic indeed that his early death prevented the completion of his work; the surviving paper on the classification and complexity of chords indicates the loss that his death meant to the area, as he was almost uniquely qualified to bring mathematics and music together, being a professional in both fields.