Topic
Magic square
About: Magic square is a research topic. Over the lifetime, 764 publications have been published within this topic receiving 7395 citations. The topic is also known as: diagonally magic square & normal magic square.
Papers published on a yearly basis
Papers
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01 Jan 1974
TL;DR: Latin Squares and Their Applications Second edition offers a long-awaited update and reissue of this seminal account of the subject, which retains foundational, original material from the frequently-cited 1974 volume but is completely updated throughout.
Abstract: 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
962 citations
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01 Jul 2007
TL;DR: The Ehrhart Theory of Reciprocity as discussed by the authors has been applied to count lattice points in polytopes and the Dehn-Sommerville relations.
Abstract: Preface.- The Coin-Exchange Problem of Frobenius.- A Gallery of Discrete Volumes.- Counting Lattice Points in Polytopes: The Ehrhart Theory.- Reciprocity.- Face Numbers and the Dehn-Sommerville Relations in Ehrhartian Terms.- Magic Squares.- Finite Fourier Analysis.- Dedekind Sums.- The Decomposition of a Polytope into Its Cones.- Euler-MacLaurin Summation in Rd.- Solid Angles.- A Discrete Version of Green's Theorem Using Elliptic Functions.- Appendix A: Triangulations of Polytopes.- Appendix B: Hints for Selected Exercises.- References.- Index.- List of Symbols.-
458 citations
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TL;DR: The magic square of Freudenthal, Rozenfeld, and Tits was derived from the geometry of a special class of N = 2 Maxwell-Einstein supergravity theories.
342 citations
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03 Sep 1998
TL;DR: A Brief Introduction to Latin Squares Mutually Orthogonal Latin Square Graphs and Latin Square Graphs as discussed by the authors Theoretical Applications of Latin Squars Appendices Indexes
Abstract: LATIN SQUARES A Brief Introduction to Latin Squares Mutually Orthogonal Latin Squares GENERALIZATIONS Orthogonal Hypercubes Frequency Squares RELATED MATHEMATICS Principle of Inclusion--Exclusion Groups and Latin Squares Graphs and Latin Squares APPLICATIONS Affine and Projective Planes Orthogonal Hypercubes and Affine Designs Magic Squares Room Squares Statistics Error--Correcting Codes Cryptology (t,m,s)--Nets Miscellaneous Applications of Latin Squares Appendices Indexes
266 citations
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01 Jan 2001
TL;DR: The second edition of as discussed by the authors contains a new chapter on magic labeling of directed graphs and interesting counting arguments new research problems and exercises covering a range of difficulties a fully updated bibliography and index This concise, selfcontained exposition is unique in its focus on the theory of magic graphs/labelings.
Abstract: Magic squares are among the more popular mathematical recreations. Over the last 50 years, many generalizations of magic ideas have been applied to graphs. Recently there has been a resurgence of interest in magic labelings due to a number of results that have applications to the problem of decomposing graphs into trees. Key features of this second edition include: a new chapter on magic labeling of directed graphs applications of theorems from graph theory and interesting counting arguments new research problems and exercises covering a range of difficulties a fully updated bibliography and index This concise, self-contained exposition is unique in its focus on the theory of magic graphs/labelings. It may serve as a graduate or advanced undergraduate text for courses in mathematics or computer science, and as reference for the researcher.
266 citations