5 edition of Latin squares found in the catalog.
1991 by North-Holland, Distributors for the U.S. and Canada, Elsevier Science Pub. Co. in Amsterdam, New York, New York, N.Y., U.S.A .
Written in English
Includes bibliographical references (p. 399-443) and index.
|Statement||[edited by] J. Dénes and A.D. Keedwell ; with specialist contributions by G.B. Belyavskaya ... [et al.].|
|Series||Annals of discrete mathematics ;, 46|
|Contributions||Dénes, J., Keedwell, A. D., Beli͡a︡vskai͡a︡, G. B.|
|LC Classifications||QA165 .L38 1991|
|The Physical Object|
|Pagination||xiv, 453 p. :|
|Number of Pages||453|
|LC Control Number||90021564|
Latin squares, or sets of mutually orthogonal latin squares MOLSencode 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. But I love it for the "Latin squares". If we systematically and consistently reorder the three items in each triple, another orthogonal array and, thus, another Latin square is obtained. But in latin square B there is no symbol which is part of six 2 by 2 subtables which are latin squares.
MIT Press. This game was the last one I had left to check out. In Section 2 we secure bounds for the number of constraints which are the counterpart of the familiar theorem which states that the number of mutually orthogonal Latin squares of side s is bounded above by s - 1. From there, it describes the existence problem for complete mappings of groups, building up to the proof of the Hall—Paige conjecture. The second square is the transpose of the first square. Its focus is on orthomorphisms and complete mappings of finite groups, while also offering a complete proof of the Hall—Paige conjecture.
The Number of 9 x 9 Latin Squares. A Latin square is reduced when the first row and first column are in lexicographic order. Let Ln be the number of latin squares of order n and let Rn be the number of reduced latin squares of order n. He is the author of some ninety research papers and two books, most related in some way to latin squares. Date published: Rated 5 out of 5 by hatshepsut from Good Game Easy controls.
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Thus there aredistinct Latin squares of order 5. Bell System Technical Journal. II Technometrics. Latin squares, or sets of mutually orthogonal latin squares MOLSencode 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.
I Canadian Journal of Mathematics. This option is only really used for checking the randomness of the squares. Technical Validation The Latin square ANOVA for three factors without interaction is calculated as follows Armitage and Berry, ; Cochran and Cox, : - where Xijk is the observation from the ith row of the jth column with the kth treatment, G is the grand total of all observations, Ri is the total for the ith row, Cj is the total for the jth column, Tk is the total for the kth treatment, SStotal is the total sum of squares, SSrows is the sum of squares due to the rows, SScolumns is the sum of squares due to the columns, SStreatments is the sum of squares due to the treatments and a is the number of rows, columns or treatments.
Conversely it may be noted that any square orthogonal to these two squares must be a Latin square. Thus the binary operation system [omega]. In this case, we arbitrarily break deadlock by partitioning one of the sub-matrices between its first and second columns and then proceed normally.
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. Alternative versions of orthogonality An n x n square array L of n2 symbols taken out of [omega] is called a Latin square over [omega] or Latin square of order n if there is no repetition of symbols in each row and in each column of L.
Since the mid s, his primary research has been on orthomorphisms and complete mappings of finite groups and their applications. The method is based on the concept of orthogonal mappings of a group, due to Mann . I decided to try the few that are available here.
There may be an elegant way out there to do it, but I am not aware of it. Further details are given by Cochran and Cox What a pleasant surprise.
Orthogonal Arrays of Strength Two and Three. Also, they provide a number of ways of constructing magic squares, both simple magic squares and also ones with additional properties.
This affords another major improvement in that it is not necessary to attempt to reduce one matrix to another at each comparison.
Loved the game because you could also switch over to traditional. The Latin squares book of squares is then the sum of counts over all equivalence classes.
A function for generating Latin squares This function generates Latin squares. At each step, the sub-matrix to be operated on is selected by a set of well-defined rules.Search the world's most comprehensive index of full-text books.
My library. A Latin subsquare of a given Latin square of order is a submatrix of it such that it is itself a Latin square of order. Any Latin square of order can be a Latin subsquare of a Latin square of order if. In the construction of orthogonal Latin squares an important role is played by the concept of a transversal of a Latin square.
"This book is a comprehensive account of the subject of latin squares (and latin rectangles), by two experts. The book is written in a fairly condensed but readable ‘narrative style’. It is packed with information, either expounded in detail or with full references to the literature."Cited by: Jul 25, · Latin Squares and Their Applications is an attempt at an exhaustive study of the subject.
There is enough to say to fill pages plus a page bibliography (and the authors admit that even this bibliography is not comprehensive). Latin squares have a long history, stretching back at least as far as medieval Islam (c), when they were used on amulets.
Abu l'Abbas al Buni wrote about them and constructed, for example, 4 × 4 Latin squares using letters from a name of God. An intuitive and accessible approach to discrete mathematics using Latin squares In the past two decades, researchers have discovered a range of uses for Latin squares that go beyond standard mathematics.
People working in the fields of science, engineering, statistics, and even computer science all stand to benefit from a working knowledge of Latin atlasbowling.coms: 1.