Semi-latin squares and related objects
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Semi-latin squares and related objects statistics and combinatorics aspects : an inaugural lecture of the University of Nigeria, delivered on January 26, 2009 by Polycarp E. Chigbu

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Published by University of Nigeria, Senate Ceremonials Committee in Nsukka, Nigeria .
Written in English


Book details:

Edition Notes

Includes bibliographical references (p. 56-64).

Statementby Polycarp E. Chigbu.
SeriesInaugural lecture / University of Nigeria -- 43rd
Classifications
LC ClassificationsMLCS 2010/40143
The Physical Object
Pagination69 p. :
Number of Pages69
ID Numbers
Open LibraryOL24025166M
LC Control Number2009404226

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Purchase Latin Squares and their Applications - 2nd Edition. Print Book & E-Book. ISBN , they encapsulate the structure of finite groups and of more general algebraic objects known as quasigroups. He is the author of some ninety research papers and two books, most related in some way to latin squares. He is a Price: $ 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. Purchase Latin Squares - 1st Edition. Print Book & E-Book. ISBN , Price: $ Latin squares and their applications by J. Dénes, , There's no description for this book yet. Can you add one? Edition Notes Classifications Dewey Decimal Class /25 Library of Congress QAD42 c The Physical Object Pagination p.: Number of pages ID Numbers Open Library OLM ISBN

representation of a Latin square is normally a square grid of cells, each cell containing a symbol. For example, here is a 4x4 Latin square on the symbols α, β, χ, and δ. α β χ δ χ δ α β δ χ β α β α δ χ The symbols in a Latin square are arbitrary. Symbols can be numbers, letters, geometric shapes, and colors. Another book on Latin Squares, Discrete Mathematics Using Latin Squares by Laywine and Mullen. seems (at least according to the table of contents) to discuss a few more applications. Latin Squares and Their Applications is far from the leisurely read about Sudoku that I thought it might be. What I did get is an in-depth summary of the extensive. Bailey and Cameron (see also the CRC Handbook) discuss combinatorial objects equivalent to Latin squares. Wikipedia host a list of problems in the theory of Latin squares. The number of derangements is related to the number of Latin rectangles by Riordan gave the credit to Yamamoto for the equation Let be a prime. Stones and Wanless. Latin squares and quasigroups are equivalent mathematical objects, although the former has a combinatorial nature while the latter is more listing below will consider the examples of some very small orders, which is the side length of the square, or the number of elements in the equivalent quasigroup.

A semi-Latin square formed in the way is called a Trojan square. Example is a Trojan square (corresponding to Example 2.I with symbols distinguished). Details on maximal k for n £ n Trojan squares are in section 3. For n = 6, the best semi-Latin square for k = 2 is reported in Bailey and Royle (). Bailey () gives. In 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. Latin Squares. Introduction. It's a perpetual wonder that mathematical theories developed with no useful purpose in mind except to satisify a mathematical curiosity, often and most unexpectedly apply not only to other parts of mathematics but to other sciences and real world problems. Non-euclidean geometries became an integral part of the General Theory of Relativity. The definition of a Latin square can be written in terms of orthogonal arrays: A Latin square is a set of n 2 triples (r, c, s), where 1 ≤ r, c, s ≤ n, such that all ordered pairs (r, c) are distinct, all ordered pairs (r, s) are distinct, and all ordered pairs (c, s) are distinct.; This means that the n 2 ordered pairs (r, c) are all the pairs (i, j) with 1 ≤ i, j ≤ n, once each.