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 Graph Theory and Its Applications Second Edition written by Jonathan L. Gross and published by CRC Press. This book was released on 2005-09-22 with total page 799 pages. Available in PDF, EPUB and Kindle. Book excerpt: Already an international bestseller, with the release of this greatly enhanced second edition, Graph Theory and Its Applications is now an even better choice as a textbook for a variety of courses -- a textbook that will continue to serve your students as a reference for years to come. The superior explanations, broad coverage, and abundance of illustrations and exercises that positioned this as the premier graph theory text remain, but are now augmented by a broad range of improvements. Nearly 200 pages have been added for this edition, including nine new sections and hundreds of new exercises, mostly non-routine. What else is new? New chapters on measurement and analytic graph theory Supplementary exercises in each chapter - ideal for reinforcing, reviewing, and testing. Solutions and hints, often illustrated with figures, to selected exercises - nearly 50 pages worth Reorganization and extensive revisions in more than half of the existing chapters for smoother flow of the exposition Foreshadowing - the first three chapters now preview a number of concepts, mostly via the exercises, to pique the interest of reader Gross and Yellen take a comprehensive approach to graph theory that integrates careful exposition of classical developments with emerging methods, models, and practical needs. Their unparalleled treatment provides a text ideal for a two-semester course and a variety of one-semester classes, from an introductory one-semester course to courses slanted toward classical graph theory, operations research, data structures and algorithms, or algebra and topology.

Download or read book Introduction to Combinatorics written by Walter D. Wallis and published by CRC Press. This book was released on 2016-12-12 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Download or read book Smart Geotechnics for Smart Societies written by Askar Zhussupbekov and published by CRC Press. This book was released on 2023-08-04 with total page 4162 pages. Available in PDF, EPUB and Kindle. Book excerpt: Smart Geotechnics for Smart Societies contains the contributions presented at the 17th Asian Regional Conference on Soil Mechanics and Geotechnical Engineering (17th ARC, Astana, Kazakhstan, 14-18 August, 2023). The topics covered include: - Geomaterials for soil improvement - Tunneling and rock engineering - Slope, embankments and dams - Shallow and deep foundations - Soil dynamics and geotechnical earthquake engineering - Geoenvironmental engineering and frost geotechnics - Investigation of foundations of historical structures and monitoring - Offshore, harbor geotechnics and GeoEnergy - Megaprojects and transportation geotechnics Smart Geotechnics for Smart Societies will be of interest to academics and engineers interested or involved in geotechnical engineering.

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 Elements of Quasigroup Theory and Applications written by Victor Shcherbacov and published by CRC Press. This book was released on 2017-05-12 with total page 576 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to quasigroup theory along with new structural results on some of the quasigroup classes. Many results are presented with some of them from mathematicians of the former USSR. These included results have not been published before in the western mathematical literature. In addition, many of the achievements obtained with regard to applications of quasigroups in coding theory and cryptology are described.

Download or read book Design Theory written by Charles C. Lindner and published by CRC Press. This book was released on 2017-03-27 with total page 315 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Research Methodology Concepts and Cases 2nd Edition written by Chawla Deepak & Neena Sodhi and published by Vikas Publishing House. This book was released on with total page 820 pages. Available in PDF, EPUB and Kindle. Book excerpt: RESEARCH METHODOLOGY CONCEPT AND CASES provides a comprehensive and stepwise understanding of the research process with a balanced blend of theory, techniques and Indian illustrations from a wide cross-section of business areas. This book makes no presumptions and can be used with confidence and conviction by both students and experienced managers who need to make business sense of the data and information that is culled out through research groups. The conceptual base has been provided in comprehensive, yet simplistic detail, addressing even the minutest explanations required by the reader. The language maintains a careful balance between technical know-how and business jargon. Every chapter is profusely illustrated with business problems related to all domains—marketing, finance, human resource and operations. Thus, no matter what the interest area may be, the universal and adaptable nature of the research process is concisely demonstrated.

Download or read book A First Course in Discrete Mathematics written by Brian Lian and published by Springer Science & Business Media. This book was released on 2000-10-27 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: Drawing on many years'experience of teaching discrete mathem atics to students of all levels, Anderson introduces such as pects as enumeration, graph theory and configurations or arr angements. Starting with an introduction to counting and rel ated problems, he moves on to the basic ideas of graph theor y with particular emphasis on trees and planar graphs. He de scribes the inclusion-exclusion principle followed by partit ions of sets which in turn leads to a study of Stirling and Bell numbers. Then follows a treatment of Hamiltonian cycles, Eulerian circuits in graphs, and Latin squares as well as proof of Hall's theorem. He concludes with the constructions of schedules and a brief introduction to block designs. Each chapter is backed by a number of examples, with straightforw ard applications of ideas and more challenging problems.

Download or read book Introduction to Coding Theory written by Ron Roth and published by Cambridge University Press. This book was released on 2006-02-23 with total page 592 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 2006 book introduces the theoretical foundations of error-correcting codes for senior-undergraduate to graduate students.

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 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 Abstract Algebra written by Derek J.S. Robinson and published by Walter de Gruyter GmbH & Co KG. This book was released on 2022-02-07 with total page 506 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a high level introduction to abstract algebra which is aimed at readers whose interests lie in mathematics and the information and physical sciences. In addition to introducing the main concepts of modern algebra – groups, rings, modules and fields – the book contains numerous applications, which are intended to illustrate the concepts and to show the utility and relevance of algebra today. In particular applications to Polya coloring theory, latin squares, Steiner systems, error correcting codes and economics are described. There is ample material here for a two semester course in abstract algebra. Proofs of almost all results are given. The reader led through the proofs in gentle stages. There are more than 500 problems, of varying degrees of diffi culty. The book should be suitable for advanced undergraduate students in their fi nal year of study and for fi rst or second year graduate students at a university in Europe or North America. In this third edition three new chapters have been added: an introduction to the representation theory of fi nite groups, free groups and presentations of groups, an introduction to category theory.

Download or read book Encyclopaedia of Mathematics written by Michiel Hazewinkel and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 506 pages. Available in PDF, EPUB and Kindle. Book excerpt: This ENCYCLOPAEDIA OF MA THEMA TICS aims to be a reference work for all parts of mathe matics. It is a translation with updates and editorial comments of the Soviet Mathematical Encyclopaedia published by 'Soviet Encyclopaedia Publishing House' in five volumes in 1977-1985. The annotated translation consists of ten volumes including a special index volume. There are three kinds of articles in this ENCYCLOPAEDIA. First of all there are survey-type articles dealing with the various main directions in mathematics (where a rather fine subdivi sion has been used). The main requirement for these articles has been that they should give a reasonably complete up-to-date account of the current state of affairs in these areas and that they should be maximally accessible. On the whole, these articles should be understandable to mathematics students in their first specialization years, to graduates from other mathematical areas and, depending on the specific subject, to specialists in other domains of science, en gineers and teachers of mathematics. These articles treat their material at a fairly general level and aim to give an idea of the kind of problems, techniques and concepts involved in the area in question. They also contain background and motivation rather than precise statements of precise theorems with detailed definitions and technical details on how to carry out proofs and constructions. The second kind of article, of medium length, contains more detailed concrete problems, results and techniques.

Download or read book Discrete Mathematics with Proof written by Eric Gossett and published by John Wiley & Sons. This book was released on 2009-06-22 with total page 932 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Trusted Guide to Discrete Mathematics with Proof?Now in a Newly Revised Edition Discrete mathematics has become increasingly popular in recent years due to its growing applications in the field of computer science. Discrete Mathematics with Proof, Second Edition continues to facilitate an up-to-date understanding of this important topic, exposing readers to a wide range of modern and technological applications. The book begins with an introductory chapter that provides an accessible explanation of discrete mathematics. Subsequent chapters explore additional related topics including counting, finite probability theory, recursion, formal models in computer science, graph theory, trees, the concepts of functions, and relations. Additional features of the Second Edition include: An intense focus on the formal settings of proofs and their techniques, such as constructive proofs, proof by contradiction, and combinatorial proofs New sections on applications of elementary number theory, multidimensional induction, counting tulips, and the binomial distribution Important examples from the field of computer science presented as applications including the Halting problem, Shannon's mathematical model of information, regular expressions, XML, and Normal Forms in relational databases Numerous examples that are not often found in books on discrete mathematics including the deferred acceptance algorithm, the Boyer-Moore algorithm for pattern matching, Sierpinski curves, adaptive quadrature, the Josephus problem, and the five-color theorem Extensive appendices that outline supplemental material on analyzing claims and writing mathematics, along with solutions to selected chapter exercises Combinatorics receives a full chapter treatment that extends beyond the combinations and permutations material by delving into non-standard topics such as Latin squares, finite projective planes, balanced incomplete block designs, coding theory, partitions, occupancy problems, Stirling numbers, Ramsey numbers, and systems of distinct representatives. A related Web site features animations and visualizations of combinatorial proofs that assist readers with comprehension. In addition, approximately 500 examples and over 2,800 exercises are presented throughout the book to motivate ideas and illustrate the proofs and conclusions of theorems. Assuming only a basic background in calculus, Discrete Mathematics with Proof, Second Edition is an excellent book for mathematics and computer science courses at the undergraduate level. It is also a valuable resource for professionals in various technical fields who would like an introduction to discrete mathematics.

Download or read book Combinatorial Designs and Applications written by W.D. Wallis and published by CRC Press. This book was released on 2020-12-22 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: An advanced reference containing 21 selected or consolidated papers presented at an international conference in April 1988 at Tunxi (now Hunangshan), China. Contains recent, previously unavailable findings of Chinese mathematicians; discusses problems, results, and proving methods of combinatorial d

Download or read book MATHEMATICAL COMBINATORICS INTERNATIONAL BOOK SERIES VOLUME 3 2015 written by L. Mao and published by Infinite Study. This book was released on with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contents A Calculus and Algebra Derived from Directed Graph Algebras By Kh.Shahbazpour and Mahdihe Nouri . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 01 Superior Edge Bimagic Labelling By R.Jagadesh and J.Baskar Babujee . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 Spherical Images of Special Smarandache Curves in E3 By Vahide Bulut and Ali Caliskan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 Variations of Orthogonality of Latin Squares By Vadiraja Bhatta G.R. and B.R.Shankar. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .55 The Minimum Equitable Domination Energy of a Graph By P.Rajendra and R.Rangarajan. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 Some Results on Relaxed Mean Labeling By V.Maheswari, D.S.T.Ramesh and V.Balaji . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 Split Geodetic Number of a Line Graph By Venkanagouda M Goudar and Ashalatha K.S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 Skolem Difference Odd Mean Labeling For Some Simple Graphs By R.Vasuki, J.Venkateswari and G.Pooranam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 Radio Number for Special Family of Graphs with Diameter 2, 3 and 4 By M.Murugan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 Vertex-to-Edge-set Distance Neighborhood Pattern Matrices By Kishori P.Narayankar and Lokesh S. B. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 Extended Results on Complementary Tree Domination Number and Chromatic Number of Graphs By S.Muthammai and P.Vidhya . . . . . . . . . . . . . . . . . . . . . . . 116 On Integer Additive Set-Sequential Graphs By N.K.Sudev and K.A.Germina . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125