Download or read book On Structure Preserving Groups of Latin Squares and Their Applications to Statistics written by Shin-Sun Chow and published by . This book was released on 1979 with total page 134 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 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 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.
Download or read book Dissertation Abstracts International written by and published by . This book was released on 1980 with total page 594 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book American Doctoral Dissertations written by and published by . This book was released on 1979 with total page 596 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Bulletin Institute of Mathematical Statistics written by Institute of Mathematical Statistics and published by . This book was released on 1981 with total page 688 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Latin Squares and Their Applications written by József Dénes and published by . This book was released on 1974 with total page 547 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Some Aspects Of Latin Squares And Their Applications written by N. Naga Syamala and published by LAP Lambert Academic Publishing. This book was released on 2014-01 with total page 92 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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'.
Download or read book Comprehensive Dissertation Index written by and published by . This book was released on 1984 with total page 904 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Latin Squares and Their Applications Second Edition written by and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Comprehensive Dissertation Index Mathematics statistics Physics A E written by and published by . This book was released on 1984 with total page 1008 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Latin Squares Their Geometries and Their Groups a Survey written by D. (Dieter) Jungnickel and published by . This book was released on 1988 with total page 69 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Orthogonal Sets of Latin Squares and Class r Hypercubes Generated By Finite Algebraic Systems written by Daniel Droz and published by . This book was released on 2016 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Latin squares are combinatorial objects which have applications in some various and slightly surprising settings. A latin square of order n is a square array on n symbols such that each symbol occurs once in each row and column. Two latin squares are called orthogonal when superimposing them gives each of the n2 ordered pairs of symbols exactly once. It is well known that if q is a prime power, the squares formed from the polynomials ax + y, a \in \mathbb{F}_q form q-1 latin squares of order q which are mutually orthogonal (each pair of squares is orthogonal). In this dissertation, we explore four problems relating to latin squares and other objects with similar properties, especially focusing on constructing large mutually orthogonal sets. We explore the extent to which sets of mutually orthogonal latin squares, hypercubes, and frequency squares can be obtained by polynomials over finite fields. We are able to rescue two classical conjectures of Euler and MacNeish which are false for general latin squares but which are true when out attention is restricted to polynomial-generated squares only. We also introduce the theory of the finite algebraic structures called uniform cyclic neofields, and explore the construction of sets of latin squares which are "nearly orthogonal.'' Our main result with be to give a simple construction of large sets of such nearly orthogonal squares for all even orders n where n-1 is prime. We then examine a new generalization of latin squares called class-r hypercubes which feature a larger alphabet (nr[superscript] rather than n symbols). We give solutions to several open problems in this area, most notably the construction of large mutually orthogonal sets for r ≥ 3. As our last topic, we give some partial progress toward solutions about a long-standing problem on the computability of partially filled latin cubes. Although the immediate extension of the famous Evans' conjecture seems fail for latin cubes of type 1 although it is true for latin squares, we explore what weaker versions of this conjecture can be said to hold.
Download or read book Matrix Tricks for Linear Statistical Models written by Simo Puntanen and published by Springer Science & Business Media. This book was released on 2011-08-24 with total page 504 pages. Available in PDF, EPUB and Kindle. Book excerpt: In teaching linear statistical models to first-year graduate students or to final-year undergraduate students there is no way to proceed smoothly without matrices and related concepts of linear algebra; their use is really essential. Our experience is that making some particular matrix tricks very familiar to students can substantially increase their insight into linear statistical models (and also multivariate statistical analysis). In matrix algebra, there are handy, sometimes even very simple “tricks” which simplify and clarify the treatment of a problem—both for the student and for the professor. Of course, the concept of a trick is not uniquely defined—by a trick we simply mean here a useful important handy result. In this book we collect together our Top Twenty favourite matrix tricks for linear statistical models.
Download or read book Notices of the American Mathematical Society written by American Mathematical Society and published by . This book was released on 1993 with total page 998 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Bulletin of the Institute of Combinatorics and Its Applications written by and published by . This book was released on 1999 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt:
