On The Existence Of Mutually Orthogonal Latin Squares Of Order 10

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Latin Squares and Their Applications

Author : A. Donald Keedwell
Publisher : Elsevier
ISBN 13 : 0444635580
Total Pages : 443 pages
Book Rating : 4.4/5 (446 download)

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Book Synopsis Latin Squares and Their Applications by : A. Donald Keedwell

Download or read book Latin Squares and Their Applications written by A. Donald Keedwell and published by Elsevier. This book was released on 2015-07-28 with total page 443 pages. Available in PDF, EPUB and Kindle. Book 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 - Includes the original 73 'Unsolved Problems' with the current state of knowledge regarding them, as well as new Unsolved Problems for further study

Design Theory

Author : Zhe-xian Wan
Publisher : World Scientific Publishing Company
ISBN 13 : 9813107650
Total Pages : 234 pages
Book Rating : 4.8/5 (131 download)

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Book Synopsis Design Theory by : Zhe-xian Wan

Download or read book Design Theory written by Zhe-xian Wan and published by World Scientific Publishing Company. This book was released on 2009-11-11 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with the basic subjects of design theory. It begins with balanced incomplete block designs, various constructions of which are described in ample detail. In particular, finite projective and affine planes, difference sets and Hadamard matrices, as tools to construct balanced incomplete block designs, are included. Orthogonal latin squares are also treated in detail. Zhu's simpler proof of the falsity of Euler's conjecture is included. The construction of some classes of balanced incomplete block designs, such as Steiner triple systems and Kirkman triple systems, are also given. T-designs and partially balanced incomplete block designs (together with association schemes), as generalizations of balanced incomplete block designs, are included. Some coding theory related to Steiner triple systems are clearly explained. The book is written in a lucid style and is algebraic in nature. It can be used as a text or a reference book for graduate students and researchers in combinatorics and applied mathematics. It is also suitable for self-study.

Latin Squares

Author : József Dénes
Publisher : Elsevier
ISBN 13 : 0080867863
Total Pages : 469 pages
Book Rating : 4.0/5 (88 download)

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Book Synopsis Latin Squares by : József Dénes

Download or read book Latin Squares written by József Dénes and published by Elsevier. This book was released on 1991-01-24 with total page 469 pages. Available in PDF, EPUB and Kindle. Book 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.

Introduction to Combinatorics

Author : Gerald Berman
Publisher : Elsevier
ISBN 13 : 1483273822
Total Pages : 315 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Introduction to Combinatorics by : Gerald Berman

Download or read book Introduction to Combinatorics written by Gerald Berman and published by Elsevier. This book was released on 2014-05-10 with total page 315 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to Combinatorics focuses on the applications, processes, methodologies, and approaches involved in combinatorics or discrete mathematics. The book first offers information on introductory examples, permutations and combinations, and the inclusion-exclusion principle. Discussions focus on some applications of the inclusion-exclusion principle, derangements, calculus of sets, permutations, combinations, Stirling's formula, binomial theorem, regions of a plane, chromatic polynomials, and a random walk. The text then examines linear equations with unit coefficients, recurrence relations, and generating functions. Topics include derivatives and differential equations, solution of difference equations by means of generating functions, recurrence relations, summation method, difference methods, combinations with repetitions, solutions bounded below, and solutions bounded above and below. The publication takes a look at generating functions and difference equations, ramifications of the binomial theorem, finite structures, coloring problems, maps on a sphere, and geometry of the plane. The manuscript is a valuable reference for researchers interested in combinatorics.

Computational Problems in Abstract Algebra

Author : John Leech
Publisher : Elsevier
ISBN 13 : 1483159426
Total Pages : 413 pages
Book Rating : 4.4/5 (831 download)

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Book Synopsis Computational Problems in Abstract Algebra by : John Leech

Download or read book Computational Problems in Abstract Algebra written by John Leech and published by Elsevier. This book was released on 2014-05-17 with total page 413 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computational Problems in Abstract Algebra provides information pertinent to the application of computers to abstract algebra. This book discusses combinatorial problems dealing with things like generation of permutations, projective planes, orthogonal latin squares, graphs, difference sets, block designs, and Hadamard matrices. Comprised of 35 chapters, this book begins with an overview of the methods utilized in and results obtained by programs for the investigation of groups. This text then examines the method for establishing the order of a finite group defined by a set of relations satisfied by its generators. Other chapters describe the modification of the Todd–Coxeter coset enumeration process. This book discusses as well the difficulties that arise with multiplication and inverting programs, and of some ways to avoid or overcome them. The final chapter deals with the computational problems related to invariant factors in linear algebra. Mathematicians as well as students of algebra will find this book useful.

The SAGE Encyclopedia of Research Design

Author : Bruce B. Frey
Publisher : SAGE Publications
ISBN 13 : 1071812106
Total Pages : 3889 pages
Book Rating : 4.0/5 (718 download)

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Book Synopsis The SAGE Encyclopedia of Research Design by : Bruce B. Frey

Download or read book The SAGE Encyclopedia of Research Design written by Bruce B. Frey and published by SAGE Publications. This book was released on 2022-01-27 with total page 3889 pages. Available in PDF, EPUB and Kindle. Book excerpt: The SAGE Encyclopedia of Research Design maps out how one makes decisions about research design, interprets data, and draws valid inferences, undertakes research projects in an ethical manner, and evaluates experimental design strategies and results. From A-to-Z, this four-volume work covers the spectrum of research design strategies and topics including, among other things: fundamental research design principles, ethics in the research process, quantitative versus qualitative and mixed-method designs, completely randomized designs, multiple comparison tests, diagnosing agreement between data and models, fundamental assumptions in analysis of variance, factorial treatment designs, complete and incomplete block designs, Latin square and related designs, hierarchical designs, response surface designs, split-plot designs, repeated measures designs, crossover designs, analysis of covariance, statistical software packages, and much more. Research design, with its statistical underpinnings, can be especially daunting for students and novice researchers. At its heart, research design might be described simply as a formalized approach toward problem solving, thinking, and acquiring knowledge, the success of which depends upon clearly defined objectives and appropriate choice of statistical design and analysis to meet those objectives. The SAGE Encyclopedia of Research Design will assist students and researchers with their work while providing vital information on research strategies.

Handbook of Combinatorial Designs

Author : C. J. Colbourn
Publisher : Chapman and Hall/CRC
ISBN 13 : 9781584885061
Total Pages : 1016 pages
Book Rating : 4.8/5 (85 download)

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Book Synopsis Handbook of Combinatorial Designs by : C. J. Colbourn

Download or read book Handbook of Combinatorial Designs written by C. J. Colbourn and published by Chapman and Hall/CRC. This book was released on 2006-11-02 with total page 1016 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 results. Over 30% longer than the first edition, the book builds upon the groundwork of its predecessor while retaining the original contributors' expertise. The first part contains a brief introduction and history of the subject. The following parts focus on four main classes of combinatorial designs: balanced incomplete block designs, orthogonal arrays and Latin squares, pairwise balanced designs, and Hadamard and orthogonal designs. Closely connected to the preceding sections, the next part surveys 65 additional classes of designs, such as balanced ternary, factorial, graphical, Howell, quasi-symmetric, and spherical. The final part presents mathematical and computational background related to design theory. New to the Second Edition An introductory part that provides a general overview and a historical perspective of the area New chapters on the history of design theory, various codes, bent functions, and numerous types of designs Fully updated tables, including BIBDs, MOLS, PBDs, and Hadamard matrices Nearly 2,200 references in a single bibliographic section Meeting the need for up-to-date and accessible tabular and reference information, this handbook provides the tools to understand combinatorial design theory and applications that span the entire discipline. The author maintains a website with more information.

Combinatorial Optimization and Applications

Author : Weili Wu
Publisher : Springer Nature
ISBN 13 : 3031496140
Total Pages : 505 pages
Book Rating : 4.0/5 (314 download)

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Book Synopsis Combinatorial Optimization and Applications by : Weili Wu

Download or read book Combinatorial Optimization and Applications written by Weili Wu and published by Springer Nature. This book was released on 2024-01-09 with total page 505 pages. Available in PDF, EPUB and Kindle. Book excerpt: The two-volume set LNCS 14461 and LNCS 14462 constitutes the refereed proceedings of the 17th International Conference on Combinatorial Optimization and Applications, COCOA 2023, held in Hawaii, HI, USA, during December 15–17, 2023. The 73 full papers included in the proceedings were carefully reviewed and selected from 117 submissions. They were organized in topical sections as follows: Part I: Optimization in graphs; scheduling; set-related optimization; applied optimization and algorithm; Graph planer and others; Part II: Modeling and algorithms; complexity and approximation; combinatorics and computing; optimization and algorithms; extreme graph and others; machine learning, blockchain and others.

Combinatorics and Finite Geometry

Author : Steven T. Dougherty
Publisher : Springer Nature
ISBN 13 : 3030563952
Total Pages : 374 pages
Book Rating : 4.0/5 (35 download)

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Book Synopsis Combinatorics and Finite Geometry by : Steven T. Dougherty

Download or read book Combinatorics and Finite Geometry written by Steven T. Dougherty and published by Springer Nature. This book was released on 2020-10-30 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: This undergraduate textbook is suitable for introductory classes in combinatorics and related topics. The book covers a wide range of both pure and applied combinatorics, beginning with the very basics of enumeration and then going on to Latin squares, graphs and designs. The latter topic is closely related to finite geometry, which is developed in parallel. Applications to probability theory, algebra, coding theory, cryptology and combinatorial game theory comprise the later chapters. Throughout the book, examples and exercises illustrate the material, and the interrelations between the various topics is emphasized. Readers looking to take first steps toward the study of combinatorics, finite geometry, design theory, coding theory, or cryptology will find this book valuable. Essentially self-contained, there are very few prerequisites aside from some mathematical maturity, and the little algebra required is covered in the text. The book is also a valuable resource for anyone interested in discrete mathematics as it ties together a wide variety of topics.

Discrete Mathematics Using Latin Squares

Author : Charles F. Laywine
Publisher : John Wiley & Sons
ISBN 13 : 9780471240648
Total Pages : 336 pages
Book Rating : 4.2/5 (46 download)

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Book Synopsis Discrete Mathematics Using Latin Squares by : Charles F. Laywine

Download or read book Discrete Mathematics Using Latin Squares written by Charles F. Laywine and published by John Wiley & Sons. This book was released on 1998-09-17 with total page 336 pages. Available in PDF, EPUB and Kindle. Book 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.

Combinatorial Matrix Theory

Author : Richard A. Brualdi
Publisher : Cambridge University Press
ISBN 13 : 9780521322652
Total Pages : 384 pages
Book Rating : 4.3/5 (226 download)

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Book Synopsis Combinatorial Matrix Theory by : Richard A. Brualdi

Download or read book Combinatorial Matrix Theory written by Richard A. Brualdi and published by Cambridge University Press. This book was released on 1991-07-26 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, first published in 1991, is devoted to the exposition of combinatorial matrix theory. This subject concerns itself with the use of matrix theory and linear algebra in proving results in combinatorics (and vice versa), and with the intrinsic properties of matrices viewed as arrays of numbers rather than algebraic objects in themselves.

Noncommutative Rings and Their Applications

Author : Steven Dougherty
Publisher : American Mathematical Soc.
ISBN 13 : 147041032X
Total Pages : 280 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Noncommutative Rings and Their Applications by : Steven Dougherty

Download or read book Noncommutative Rings and Their Applications written by Steven Dougherty and published by American Mathematical Soc.. This book was released on 2015-02-20 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains the Proceedings of an International Conference on Noncommutative Rings and Their Applications, held July 1-4, 2013, at the Universite d'Artois, Lens, France. It presents recent developments in the theories of noncommutative rings and modules over such rings as well as applications of these to coding theory, enveloping algebras, and Leavitt path algebras.

Advances in Computers

Author : Marvin Zelkowitz
Publisher : Gulf Professional Publishing
ISBN 13 : 9780120121588
Total Pages : 392 pages
Book Rating : 4.1/5 (215 download)

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Book Synopsis Advances in Computers by : Marvin Zelkowitz

Download or read book Advances in Computers written by Marvin Zelkowitz and published by Gulf Professional Publishing. This book was released on 2003-08-08 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume describes various approaches towards software dependability: development measurability; transformation oriented programming; bounded model checking; GUI testing; and the evolution of the various security policies that ensure appropriate secure behaviour.

Finite Geometries

Author : Gyorgy Kiss
Publisher : CRC Press
ISBN 13 : 1498721664
Total Pages : 347 pages
Book Rating : 4.4/5 (987 download)

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Book Synopsis Finite Geometries by : Gyorgy Kiss

Download or read book Finite Geometries written by Gyorgy Kiss and published by CRC Press. This book was released on 2019-07-26 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: Finite Geometries stands out from recent textbooks about the subject of finite geometries by having a broader scope. The authors thoroughly explain how the subject of finite geometries is a central part of discrete mathematics. The text is suitable for undergraduate and graduate courses. Additionally, it can be used as reference material on recent works. The authors examine how finite geometries’ applicable nature led to solutions of open problems in different fields, such as design theory, cryptography and extremal combinatorics. Other areas covered include proof techniques using polynomials in case of Desarguesian planes, and applications in extremal combinatorics, plus, recent material and developments. Features: Includes exercise sets for possible use in a graduate course Discusses applications to graph theory and extremal combinatorics Covers coding theory and cryptography Translated and revised text from the Hungarian published version

The Genius of Euler: Reflections on his Life and Work

Author : William Dunham
Publisher : American Mathematical Soc.
ISBN 13 : 147045744X
Total Pages : 328 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis The Genius of Euler: Reflections on his Life and Work by : William Dunham

Download or read book The Genius of Euler: Reflections on his Life and Work written by William Dunham and published by American Mathematical Soc.. This book was released on 2020-08-03 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Automated Reasoning and Its Applications

Author : Robert Veroff
Publisher : MIT Press
ISBN 13 : 9780262220552
Total Pages : 276 pages
Book Rating : 4.2/5 (25 download)

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Book Synopsis Automated Reasoning and Its Applications by : Robert Veroff

Download or read book Automated Reasoning and Its Applications written by Robert Veroff and published by MIT Press. This book was released on 1997 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: The contributors are among the world's leading researchers inautomated reasoning. Their essays cover the theory, software system design, and use of these systems to solve real problems. The primary objective of automated reasoning (which includes automated deduction and automated theorem proving) is to develop computer programs that use logical reasoning for the solution of a wide variety of problems, including open questions. The essays in Automated Reasoning and Its Applications were written in honor of Larry Wos, one of the founders of the field. Wos played a central role in forming the culture of automated reasoning at Argonne National Laboratory. He and his colleagues consistently seek to build systems that search huge spaces for solutions to difficult problems and proofs of significant theorems. They have had numerous notable successes. The contributors are among the world's leading researchers in automated reasoning. Their essays cover the theory, software system design, and use of these systems to solve real problems. Contributors Robert S. Boyer, Shang-Ching Chou, Xiao-Shan Gao, Lawrence Henschen, Deepak Kapur, Kenneth Kunen, Ewing Lusk, William McCune, J Strother Moore, Ross Overbeek, Lawrence C. Paulson, Hantao Zhang, Jing-Zhong Zhang

Advances in Conceptual Modeling - Challenging Perspectives

Author : Carlos A. Heuser
Publisher : Springer Science & Business Media
ISBN 13 : 364204946X
Total Pages : 375 pages
Book Rating : 4.6/5 (42 download)

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Book Synopsis Advances in Conceptual Modeling - Challenging Perspectives by : Carlos A. Heuser

Download or read book Advances in Conceptual Modeling - Challenging Perspectives written by Carlos A. Heuser and published by Springer Science & Business Media. This book was released on 2009-10-26 with total page 375 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed joint proceedings of eight international workshops held in conjunction with the 28th International Conference on Conceptual Modeling, ER 2009, in Gramado, Brazil, in November 2009. The 33 revised full papers presented were carefully reviewed and selected from 100 submissions. Topics addressed by the workshops are active conceptual modeling of learning (ACM-L), conceptual modeling in the large (CoMoL), evolving theories of conceptual modeling (ETheCoM), workshop on foundations and practices of UML (FP-UML), joint international workshop on metamodels, ontologies, semantic technologies, and information systems for the semantic web (MOST-ONISW), quality of information systems (QoIS), requirements, Intentions and goals in conceptual modeling ( RIGiM) and semantic and conceptual issues in geographic information systems (SeCoGIS).