Download or read book On Completing and Avoiding Partial Latin Squares written by Jaromy Scott Kuhl and published by . This book was released on 2005 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Avoiding Partial Latin Squares Simultaneously written by Hannah Marie Berry and published by . This book was released on 2011 with total page 96 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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.

Download or read book On the Completion of Partial Latin Squares written by Tatsuo Oyama and published by . This book was released on 1977 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book How to Do what You Want to Do when You Can Not Do what You Want written by Lars-Daniel Öhman and published by . This book was released on 2006 with total page 9 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Related Necessary Conditions for Completing Partial Latin Squares written by Rick Giles and published by . This book was released on 1978 with total page 44 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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.

Download or read book Completing Partial Latin Squares with Two Prescribed Diagonals written by Martin Grüttmüller and published by . This book was released on 2002 with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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

Download or read book Completing Partial Latin Squares with Prescribed Diagonals written by Martin Grüttmüller and published by . This book was released on 2001 with total page 9 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Completing Partial N X N Latin Squares where Each Row Column and Symbol is Used at Most Cn Times written by Amanda Chetwynd and published by . This book was released on 1985 with total page 14 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Completing Partial Latin Squares written by Lars Døvling Andersen and published by . This book was released on 1985 with total page 60 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Completing partial nxn latin squares where each row column and symbol is used at most cn times written by Amanda Chetwynd and published by . This book was released on 1985 with total page 14 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Completing partial pairwise orthogonal latin squares written by Torbjörn Gustavsson and published by . This book was released on 1990 with total page 70 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book On Self orthogonal Latin Squares and Partial Transversals of Latin Squares written by Shinmin Patrick Wang and published by . This book was released on 1978 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Completions of Epsilon dense Partial Latin Squares written by Padraic James Bartlett and published by . This book was released on 2013 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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.