Latin Squares and Their Applications Book

Latin Squares and Their Applications


  • Author : A. Donald Keedwell
  • Publisher : Elsevier
  • Release Date : 2015-07-28
  • Genre: Mathematics
  • Pages : 455
  • ISBN 10 : 9780444635587

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Latin Squares and Their Applications 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 Inclu

Latin Squares Book

Latin Squares


  • Author : József Dénes
  • Publisher : Elsevier
  • Release Date : 1991-01-24
  • Genre: Mathematics
  • Pages : 452
  • ISBN 10 : 0080867863

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Latin Squares 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.

Some Aspects Of Latin Squares And Their Applications Book

Some Aspects Of Latin Squares And Their Applications


  • Author : N. Naga Syamala
  • Publisher : LAP Lambert Academic Publishing
  • Release Date : 2014-01
  • Genre: Uncategoriezed
  • Pages : 92
  • ISBN 10 : 3659504017

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Some Aspects Of Latin Squares And Their Applications 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'.

Discrete Mathematics Using Latin Squares Book

Discrete Mathematics Using Latin Squares


  • Author : Charles F. Laywine
  • Publisher : John Wiley & Sons
  • Release Date : 1998-09-17
  • Genre: Mathematics
  • Pages : 336
  • ISBN 10 : 0471240648

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Discrete Mathematics Using Latin Squares 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.

Orthogonal Latin Squares Based on Groups Book

Orthogonal Latin Squares Based on Groups


  • Author : Anthony B. Evans
  • Publisher : Springer
  • Release Date : 2018-08-17
  • Genre: Mathematics
  • Pages : 537
  • ISBN 10 : 9783319944302

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Orthogonal Latin Squares Based on Groups 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.

Combinatorial Designs and their Applications Book

Combinatorial Designs and their Applications


  • Author : Kathleen Quinn
  • Publisher : CRC Press
  • Release Date : 1999-01-29
  • Genre: Mathematics
  • Pages : 164
  • ISBN 10 : 0849306590

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Combinatorial Designs and their Applications Excerpt :

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 Book

Bipartite Graphs and Their Applications


  • Author : Armen S. Asratian
  • Publisher : Cambridge University Press
  • Release Date : 1998-07-13
  • Genre: Mathematics
  • Pages : 283
  • ISBN 10 : 052159345X

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Bipartite Graphs and Their Applications Excerpt :

This is the first book which deals solely with bipartite graphs. Together with traditional material, the reader will also find many new and unusual results. Essentially all proofs are given in full; many of these have been streamlined specifically for this text. Numerous exercises of all standards have also been included. The theory is illustrated with many applications especially to problems in timetabling, Chemistry, Communication Networks and Computer Science. For the most part the material is accessible to any reader with a graduate understanding of mathematics. However, the book contains advanced sections requiring much more specialized knowledge, which will be of interest to specialists in combinatorics and graph theory.

Encyclopaedia of Mathematics Book

Encyclopaedia of Mathematics


  • Author : Michiel Hazewinkel
  • Publisher : Springer Science & Business Media
  • Release Date : 2012-12-06
  • Genre: Mathematics
  • Pages : 506
  • ISBN 10 : 9789401512374

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Encyclopaedia of Mathematics Excerpt :

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.

From Great Discoveries in Number Theory to Applications Book

From Great Discoveries in Number Theory to Applications


  • Author : Michal Křížek
  • Publisher : Springer Nature
  • Release Date : 2021-09-21
  • Genre: Mathematics
  • Pages : 337
  • ISBN 10 : 9783030838997

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From Great Discoveries in Number Theory to Applications 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.

The Zen of Magic Squares  Circles  and Stars Book

The Zen of Magic Squares Circles and Stars


  • Author : Clifford A. Pickover
  • Publisher : Princeton University Press
  • Release Date : 2004-01-18
  • Genre: Mathematics
  • Pages : 427
  • ISBN 10 : 9780691115979

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The Zen of Magic Squares Circles and Stars Excerpt :

Provides a history of magic squares and similar structures, describing their construction and classification, along with informaiton on newly discovered objects.