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Latin Squares and Their Applications

Latin Squares and Their Applications
  • Author : A. Donald Keedwell,József Dénes
  • Publisher :Unknown
  • Release Date :2015-07-28
  • Total pages :455
  • ISBN : 9780444635587
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Summary : 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
  • Author : József Dénes (mathématicien).),A. D.. Keedwell
  • Publisher :Unknown
  • Release Date :1974
  • Total pages :547
  • ISBN : 012209350X
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Summary :

Latin Squares

Latin Squares
  • Author : József Dénes,A. Donald Keedwell
  • Publisher :Unknown
  • Release Date :1991-01-24
  • Total pages :452
  • ISBN : 0080867863
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Summary : 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

Some Aspects Of Latin Squares And Their Applications
  • Author : N. Naga Syamala,Balasiddamuni Pagadala,D. Chandra Kesavulu Naidu
  • Publisher :Unknown
  • Release Date :2014-01
  • Total pages :92
  • ISBN : 3659504017
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Summary : 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

Latin Squares and Their Applications
  • Author : József Dénes,A. D. Keedwell
  • Publisher :Unknown
  • Release Date :1974
  • Total pages :547
  • ISBN : 034012489X
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Summary :

Latin Squares and Their Applications (Second Edition)

Latin Squares and Their Applications (Second Edition)
  • Author : Anonim
  • Publisher :Unknown
  • Release Date :2021
  • Total pages :229
  • ISBN : OCLC:972032143
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Summary :

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
  • Publisher :Unknown
  • Release Date :1979
  • Total pages :112
  • ISBN : MSU:31293100643810
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Summary :

Handbook of Combinatorial Designs

Handbook of Combinatorial Designs
  • Author : Charles J. Colbourn,Jeffrey H. Dinitz
  • Publisher :Unknown
  • Release Date :2006-11-02
  • Total pages :1016
  • ISBN : 143983234X
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Summary : Continuing in the bestselling, informative tradition of the first edition, the Handbook of Combinatorial Designs, Second Edition remains the only resource to contain all of the most important results and tables in the field of combinatorial design. This handbook covers the constructions, properties, and applications of designs as well as existence

Latin Squares and Their Applications

Latin Squares and Their Applications
  • Author : A. Donald Keedwell,Jozsef Denes
  • Publisher :Unknown
  • Release Date :2015-07-24
  • Total pages :438
  • ISBN : 0444635556
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Summary : 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 Square Design and Their Applications

Latin Square Design and Their Applications
  • Author : G. Mokesh Rayalu,J. Ravi Sankar,A. Felix
  • Publisher :Unknown
  • Release Date :2016-12-10
  • Total pages :72
  • ISBN : 3659844268
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Summary :

Mutually Nearly Orthogonal Latin Squares and Their Applications

Mutually Nearly Orthogonal Latin Squares and Their Applications
  • Author : Elise B. Pasles
  • Publisher :Unknown
  • Release Date :2004
  • Total pages :188
  • ISBN : OCLC:58483659
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Summary :

Discrete Mathematics Using Latin Squares

Discrete Mathematics Using Latin Squares
  • Author : Charles F. Laywine,Gary L. Mullen
  • Publisher :Unknown
  • Release Date :1998-09-17
  • Total pages :305
  • ISBN : 0471240648
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Summary : 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 and Their Applications to Cryptography

Latin Squares and Their Applications to Cryptography
  • Author : Nathan O. Schmidt
  • Publisher :Unknown
  • Release Date :2016
  • Total pages :210
  • ISBN : OCLC:976412332
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Summary :

Orthogonal Arrays

Orthogonal Arrays
  • Author : A.S. Hedayat,N.J.A. Sloane,John Stufken
  • Publisher :Unknown
  • Release Date :2012-12-06
  • Total pages :417
  • ISBN : 9781461214786
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Summary : Orthogonal arrays have played a vital role in improving the quality of products manufactured throughout the world. This first book on the subject since its introduction more than fifty years ago serves as a key resource to this area of designing experiments. Most of the arrays obtained by the methods in this book are available electronically. Anyone running experiments - whether in a chemistry lab or a manufacturing plant, or in agricultural or medical research - will find this book useful.

Orthogonal Latin Squares Based on Groups

Orthogonal Latin Squares Based on Groups
  • Author : Anthony B. Evans
  • Publisher :Unknown
  • Release Date :2018-08-17
  • Total pages :537
  • ISBN : 9783319944302
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Summary : 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.

The Concise Encyclopedia of Statistics

The Concise Encyclopedia of Statistics
  • Author : Yadolah Dodge
  • Publisher :Unknown
  • Release Date :2008-04-15
  • Total pages :622
  • ISBN : 9780387317427
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Summary : The Concise Encyclopedia of Statistics presents the essential information about statistical tests, concepts, and analytical methods in language that is accessible to practitioners and students of the vast community using statistics in medicine, engineering, physical science, life science, social science, and business/economics. The reference is alphabetically arranged to provide quick access to the fundamental tools of statistical methodology and biographies of famous statisticians. The more than 500 entries include definitions, history, mathematical details, limitations, examples, references, and further readings. All entries include cross-references as well as the key citations. The back matter includes a timeline of statistical inventions. This reference will be an enduring resource for locating convenient overviews about this essential field of study.

Design of Comparative Experiments

Design of Comparative Experiments
  • Author : R. A. Bailey
  • Publisher :Unknown
  • Release Date :2008-04-17
  • Total pages :229
  • ISBN : 9781139469913
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Summary : This book should be on the shelf of every practising statistician who designs experiments. Good design considers units and treatments first, and then allocates treatments to units. It does not choose from a menu of named designs. This approach requires a notation for units that does not depend on the treatments applied. Most structure on the set of observational units, or on the set of treatments, can be defined by factors. This book develops a coherent framework for thinking about factors and their relationships, including the use of Hasse diagrams. These are used to elucidate structure, calculate degrees of freedom and allocate treatment subspaces to appropriate strata. Based on a one-term course the author has taught since 1989, the book is ideal for advanced undergraduate and beginning graduate courses. Examples, exercises and discussion questions are drawn from a wide range of real applications: from drug development, to agriculture, to manufacturing.

Design Theory

Design Theory
  • Author : Charles C. Lindner,Christopher A. Rodger
  • Publisher :Unknown
  • Release Date :2017-03-27
  • Total pages :272
  • ISBN : 9781351606455
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Summary : Design Theory, Second Edition presents some of the most important techniques used for constructing combinatorial designs. It augments the descriptions of the constructions with many figures to help students understand and enjoy this branch of mathematics. This edition now offers a thorough development of the embedding of Latin squares and combinatorial designs. It also presents some pure mathematical ideas, including connections between universal algebra and graph designs. The authors focus on several basic designs, including Steiner triple systems, Latin squares, and finite projective and affine planes. They produce these designs using flexible constructions and then add interesting properties that may be required, such as resolvability, embeddings, and orthogonality. The authors also construct more complicated structures, such as Steiner quadruple systems. By providing both classical and state-of-the-art construction techniques, this book enables students to produce many other types of designs.

Introduction to Combinatorics

Introduction to Combinatorics
  • Author : Walter D. Wallis,John C. George
  • Publisher :Unknown
  • Release Date :2016-12-12
  • Total pages :424
  • ISBN : 9781498777636
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Summary : What Is Combinatorics Anyway? Broadly speaking, combinatorics is the branch of mathematics dealing with different ways of selecting objects from a set or arranging objects. It tries to answer two major kinds of questions, namely, counting questions: how many ways can a selection or arrangement be chosen with a particular set of properties; and structural questions: does there exist a selection or arrangement of objects with a particular set of properties? The authors have presented a text for students at all levels of preparation. For some, this will be the first course where the students see several real proofs. Others will have a good background in linear algebra, will have completed the calculus stream, and will have started abstract algebra. The text starts by briefly discussing several examples of typical combinatorial problems to give the reader a better idea of what the subject covers. The next chapters explore enumerative ideas and also probability. It then moves on to enumerative functions and the relations between them, and generating functions and recurrences., Important families of functions, or numbers and then theorems are presented. Brief introductions to computer algebra and group theory come next. Structures of particular interest in combinatorics: posets, graphs, codes, Latin squares, and experimental designs follow. The authors conclude with further discussion of the interaction between linear algebra and combinatorics. Features Two new chapters on probability and posets. Numerous new illustrations, exercises, and problems. More examples on current technology use A thorough focus on accuracy Three appendices: sets, induction and proof techniques, vectors and matrices, and biographies with historical notes, Flexible use of MapleTM and MathematicaTM

Combinatorial Designs

Combinatorial Designs
  • Author : Douglas R. Stinson
  • Publisher :Unknown
  • Release Date :2007-05-08
  • Total pages :300
  • ISBN : 9780387217376
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Summary : Created to teach students many of the most important techniques used for constructing combinatorial designs, this is an ideal textbook for advanced undergraduate and graduate courses in combinatorial design theory. The text features clear explanations of basic designs, such as Steiner and Kirkman triple systems, mutual orthogonal Latin squares, finite projective and affine planes, and Steiner quadruple systems. In these settings, the student will master various construction techniques, both classic and modern, and will be well-prepared to construct a vast array of combinatorial designs. Design theory offers a progressive approach to the subject, with carefully ordered results. It begins with simple constructions that gradually increase in complexity. Each design has a construction that contains new ideas or that reinforces and builds upon similar ideas previously introduced. A new text/reference covering all apsects of modern combinatorial design theory. Graduates and professionals in computer science, applied mathematics, combinatorics, and applied statistics will find the book an essential resource.

Combinatorial Methods with Computer Applications

Combinatorial Methods with Computer Applications
  • Author : Jonathan L. Gross
  • Publisher :Unknown
  • Release Date :2007-11-16
  • Total pages :664
  • ISBN : 9781584887430
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Summary : Combinatorial Methods with Computer Applications provides in-depth coverage of recurrences, generating functions, partitions, and permutations, along with some of the most interesting graph and network topics, design constructions, and finite geometries. Requiring only a foundation in discrete mathematics, it can serve as the textbook in a combinatorial methods course or in a combined graph theory and combinatorics course. After an introduction to combinatorics, the book explores six systematic approaches within a comprehensive framework: sequences, solving recurrences, evaluating summation expressions, binomial coefficients, partitions and permutations, and integer methods. The author then focuses on graph theory, covering topics such as trees, isomorphism, automorphism, planarity, coloring, and network flows. The final chapters discuss automorphism groups in algebraic counting methods and describe combinatorial designs, including Latin squares, block designs, projective planes, and affine planes. In addition, the appendix supplies background material on relations, functions, algebraic systems, finite fields, and vector spaces. Paving the way for students to understand and perform combinatorial calculations, this accessible text presents the discrete methods necessary for applications to algorithmic analysis, performance evaluation, and statistics as well as for the solution of combinatorial problems in engineering and the social sciences.