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Author : 蔡淑慧
Publisher :
ISBN 13 :
Total Pages : 54 pages
Book Rating : 4.:/5 (837 download)
Download or read book Orthogonality of Latin Squares Defined by Abelian Groups written by 蔡淑慧 and published by . This book was released on 2008 with total page 54 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : József Dénes
Publisher : Elsevier
ISBN 13 : 0080867863
Total Pages : 469 pages
Book Rating : 4.0/5 (88 download)
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.
Author : Anthony B. Evans
Publisher : Springer
ISBN 13 : 3319944304
Total Pages : 537 pages
Book Rating : 4.3/5 (199 download)
Download or read book Orthogonal Latin Squares Based on Groups written by Anthony B. Evans and published by Springer. This book was released on 2018-08-17 with total page 537 pages. Available in PDF, EPUB and Kindle. Book 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.
Author : A. Donald Keedwell
Publisher : Elsevier
ISBN 13 : 0444635580
Total Pages : 443 pages
Book Rating : 4.4/5 (446 download)
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
Author : Charles F. Laywine
Publisher : John Wiley & Sons
ISBN 13 : 9780471240648
Total Pages : 336 pages
Book Rating : 4.2/5 (46 download)
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.
Author : A. L. Dulmage
Publisher :
ISBN 13 :
Total Pages : 92 pages
Book Rating : 4.3/5 (91 download)
Download or read book The Theory of Orthomorphisms of Groups and Orthogonal Latin Squares written by A. L. Dulmage and published by . This book was released on 1961 with total page 92 pages. Available in PDF, EPUB and Kindle. Book excerpt: Orthomorphisms are mappings of a finite group onto itself which produce latin squares orthogonal to the square which is the addition table of the group. This paper gives methods of construction of orthomorphisms, their relation to finite plane geometries and their transformation properties. The theory is applied to all groups of order up to and including 12 and to the Veblen Wedderburn projective plane of order 9.
Author : Abdossamad Hedayat
Publisher :
ISBN 13 :
Total Pages : 346 pages
Book Rating : 4.E/5 ( download)
Download or read book On the Theory of the Existence, Non-existence, and the Construction of Mutually Orthogonal F-squares and Latin Squares written by Abdossamad Hedayat and published by . This book was released on 1969 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Richard A. Brualdi
Publisher : Cambridge University Press
ISBN 13 : 9780521322652
Total Pages : 384 pages
Book Rating : 4.3/5 (226 download)
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.
Author : Raymond R Fletcher III
Publisher : Xlibris Corporation
ISBN 13 : 1664186778
Total Pages : 284 pages
Book Rating : 4.6/5 (641 download)
Download or read book Magic Polygons written by Raymond R Fletcher III and published by Xlibris Corporation. This book was released on with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: The concept of a magic square is of ancient origin; the simple 3 by 3 square called “Lo Shu” being the first to appear. The cells of a magic square are populated with consecutive positive integers in such a way that all rows and columns have the same sum. “Magic Polygons” presents a natural generalization which involves polygons with more than 4 sides. A polygon is first tiled with parallelograms with the result that sequences of parallelograms with mutually parallel sides form streams which extend from one boundary edge to an opposite boundary edge. These streams form the analog of rows and columns in a magic square: the tiles are labeled with integers so that all streams have the same sum. Instead of using the positive integers 1, 2, 3, ... to label the tiles, various abelian groups are used, thus adding a further new dimension to the constructions. Related topics such as “Latin Polygons”, “Magic Cylinders” and “Magic Circle Systems” are also introduced.
Author : Fan Chung
Publisher : CRC Press
ISBN 13 : 100075183X
Total Pages : 443 pages
Book Rating : 4.0/5 (7 download)
Download or read book 50 years of Combinatorics, Graph Theory, and Computing written by Fan Chung and published by CRC Press. This book was released on 2019-11-15 with total page 443 pages. Available in PDF, EPUB and Kindle. Book excerpt: 50 Years of Combinatorics, Graph Theory, and Computing advances research in discrete mathematics by providing current research surveys, each written by experts in their subjects. The book also celebrates outstanding mathematics from 50 years at the Southeastern International Conference on Combinatorics, Graph Theory & Computing (SEICCGTC). The conference is noted for the dissemination and stimulation of research, while fostering collaborations among mathematical scientists at all stages of their careers. The authors of the chapters highlight open questions. The sections of the book include: Combinatorics; Graph Theory; Combinatorial Matrix Theory; Designs, Geometry, Packing and Covering. Readers will discover the breadth and depth of the presentations at the SEICCGTC, as well as current research in combinatorics, graph theory and computer science. Features: Commemorates 50 years of the Southeastern International Conference on Combinatorics, Graph Theory & Computing with research surveys Surveys highlight open questions to inspire further research Chapters are written by experts in their fields Extensive bibliographies are provided at the end of each chapter
Download or read book Canadian Journal of Mathematics written by and published by . This book was released on 1961 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Ching-Shui Cheng
Publisher : CRC Press
ISBN 13 : 1466505583
Total Pages : 403 pages
Book Rating : 4.4/5 (665 download)
Download or read book Theory of Factorial Design written by Ching-Shui Cheng and published by CRC Press. This book was released on 2016-04-19 with total page 403 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bringing together both new and old results, Theory of Factorial Design: Single- and Multi-Stratum Experiments provides a rigorous, systematic, and up-to-date treatment of the theoretical aspects of factorial design. To prepare readers for a general theory, the author first presents a unified treatment of several simple designs, including completely randomized designs, block designs, and row-column designs. As such, the book is accessible to readers with minimal exposure to experimental design. With exercises and numerous examples, it is suitable as a reference for researchers and as a textbook for advanced graduate students. In addition to traditional topics and a thorough discussion of the popular minimum aberration criterion, the book covers many topics and new results not found in existing books. These include results on the structures of two-level resolution IV designs, methods for constructing such designs beyond the familiar foldover method, the extension of minimum aberration to nonregular designs, the equivalence of generalized minimum aberration and minimum moment aberration, a Bayesian approach, and some results on nonregular designs. The book also presents a theory that provides a unifying framework for the design and analysis of factorial experiments with multiple strata (error terms) arising from complicated structures of the experimental units. This theory can be systematically applied to various structures of experimental units instead of treating each on a case-by-case basis.
Author : Ronald Solomon
Publisher : World Scientific
ISBN 13 : 9814553034
Total Pages : 350 pages
Book Rating : 4.8/5 (145 download)
Download or read book Group Theory - Proceedings Of The Biennial Ohio State - Denison Conference written by Ronald Solomon and published by World Scientific. This book was released on 1993-09-30 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a collection of invited papers on the theory of groups, most of which were presented at the biennial Ohio State-Denison Conference, May 1992, in memory of Hans Zassenhaus. These papers treat important topics in the theory of p-groups, solvable groups, finitely presented groups, arithmetic groups, monodromy groups and the general structure and representation theory of groups. Of particular note are papers by John Walter on root systems, by Leonard Scott on integral equivalence of permutation representations and Alex Turull on generalized Brauer groups.
Author : W. D. Wallis
Publisher : Springer
ISBN 13 : 3540379940
Total Pages : 503 pages
Book Rating : 4.5/5 (43 download)
Download or read book Combinatorics written by W. D. Wallis and published by Springer. This book was released on 2006-11-15 with total page 503 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : J. H. van Lint
Publisher : Cambridge University Press
ISBN 13 : 9780521006019
Total Pages : 620 pages
Book Rating : 4.0/5 (6 download)
Download or read book A Course in Combinatorics written by J. H. van Lint and published by Cambridge University Press. This book was released on 2001-11-22 with total page 620 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the second edition of a popular book on combinatorics, a subject dealing with ways of arranging and distributing objects, and which involves ideas from geometry, algebra and analysis. The breadth of the theory is matched by that of its applications, which include topics as diverse as codes, circuit design and algorithm complexity. It has thus become essential for workers in many scientific fields to have some familiarity with the subject. The authors have tried to be as comprehensive as possible, dealing in a unified manner with, for example, graph theory, extremal problems, designs, colorings and codes. The depth and breadth of the coverage make the book a unique guide to the whole of the subject. The book is ideal for courses on combinatorical mathematics at the advanced undergraduate or beginning graduate level. Working mathematicians and scientists will also find it a valuable introduction and reference.
Author : R. A. Bailey
Publisher : Cambridge University Press
ISBN 13 : 9781139449939
Total Pages : 410 pages
Book Rating : 4.4/5 (499 download)
Download or read book Association Schemes written by R. A. Bailey and published by Cambridge University Press. This book was released on 2004-02-26 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: Association schemes are of interest to both mathematicians and statisticians and this book was written with both audiences in mind. For statisticians, it shows how to construct designs for experiments in blocks, how to compare such designs, and how to analyse data from them. The reader is only assumed to know very basic abstract algebra. For pure mathematicians, it tells why association schemes are important and develops the theory to the level of advanced research. This book arose from a course successfully taught by the author and as such the material is thoroughly class-tested. There are a great number of examples and exercises that will increase the book's appeal to both graduate students and their instructors. It is ideal for those coming either from pure mathematics or statistics backgrounds who wish to develop their understanding of association schemes.
Author : Beruwalage Lakshika Kumari Gunawardana
Publisher :
ISBN 13 :
Total Pages : 58 pages
Book Rating : 4.:/5 (968 download)
Download or read book A Variation on Mutually Orthogonal Latin Squares written by Beruwalage Lakshika Kumari Gunawardana and published by . This book was released on 2016 with total page 58 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Latin square of order n is an n × n array in which each row and column contains symbols from an n-set, S = {a1,..., an}, exactly once. If two Latin squares L 1 and L2 of the same order can be joined such that each of the n2 ordered pairs ( ai, aj) appears exactly once, then L1 and L2 are said to be orthogonal. This project will involve a variation of this idea. We define orthogonality of two Latin squares Lm and Ln, for m
