Latin Squares and Their Applications

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

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  • Author : A. Donald Keedwell
  • Publisher : Elsevier
  • Pages : 455 pages
  • ISBN : 0444635580
  • Rating : 4/5 from 21 reviews
CLICK HERE TO GET THIS BOOKLatin Squares and Their Applications

Latin Squares and Their Applications

Latin Squares and Their Applications
  • Author : A. Donald Keedwell,József Dénes
  • Publisher : Elsevier
  • Release : 28 July 2015
GET THIS BOOKLatin Squares and Their Applications

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

Latin Squares

Latin Squares
  • Author : József Dénes,A. Donald Keedwell
  • Publisher : Elsevier
  • Release : 24 January 1991
GET THIS BOOKLatin Squares

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

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
  • Publisher : LAP Lambert Academic Publishing
  • Release : 01 January 2014
GET THIS BOOKSome Aspects Of Latin Squares And Their Applications

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

Combinatorial Designs and their Applications

Combinatorial Designs and their Applications
  • Author : Kathleen Quinn,Bridget Webb,Chris Rowley,F C Holroyd
  • Publisher : CRC Press
  • Release : 29 January 1999
GET THIS BOOKCombinatorial Designs and their Applications

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

Designs and Graphs

Designs and Graphs
  • Author : C.J. Colbourn,D. Jungnickel,A. Rosa
  • Publisher : Elsevier
  • Release : 06 June 2016
GET THIS BOOKDesigns and Graphs

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

Finite Fields and Applications

Finite Fields and Applications
  • Author : Stephen D. Cohen
  • Publisher : Cambridge University Press
  • Release : 28 September 1996
GET THIS BOOKFinite Fields and Applications

Finite fields are algebraic structures in which there is much research interest. This book gives a state-of-the-art account of finite fields and their applications in communications (coding theory, cryptology), combinatorics, design theory, quasirandom points, algorithms and their complexity. Typically, theory and application are tightly interwoven in the survey articles and original research papers included here. The book also demonstrates interconnections with other branches of pure mathematics such as number theory, group theory and algebraic geometry. This volume is an invaluable

Orthogonal Latin Squares Based on Groups

Orthogonal Latin Squares Based on Groups
  • Author : Anthony B. Evans
  • Publisher : Springer
  • Release : 17 August 2018
GET THIS BOOKOrthogonal Latin Squares Based on Groups

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

Encyclopaedia of Mathematics

Encyclopaedia of Mathematics
  • Author : Michiel Hazewinkel
  • Publisher : Springer Science & Business Media
  • Release : 06 December 2012
GET THIS BOOKEncyclopaedia of Mathematics

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