UID:
almahu_9949697968902882
Format:
1 online resource (469 p.)
ISBN:
1-281-78947-X
,
9786611789473
,
0-08-086786-3
Series Statement:
Annals of discrete mathematics, 46
Content:
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-or
Note:
Description based upon print version of record.
,
Front Cover; Latin Squares: New Developments in the Theory and Applications; Copyright Page; CONTENTS; Preface; Acknowledgements; CHAPTER 1. INTRODUCTION; (1) Basic definitions; (2) Orthogonal latin squares; (3) Isotopy and parastrophy; CHAPTER 2. TRANSVERSALS AND COMPLETE MAPPINGS; (1) Basic facts and definitions; (2) Partial transversals; (3) Number of transversals in a latin square; (4) Sets of mutually orthogonal latin squares with no common transversal; (5) Sets of mutually orthogonal latin squares which are not extendible
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(6) Generalizations of the concepts of transversal and complete mappingADDITIONAL REMARKS; CHAPTER 3. SEQUENCEABLE AND R-SEQUENCEABLE GROUPS: ROW COMPLETE LATIN SQUARES; (1) Row-complete latin squares and sequenceable groups; (2) Quasi-complete latin squares, terraces and quasi- sequenceable groups; (3) R-sequenceable and Rh-sequenceable groups; (4) Super P-groups; (5) Tuscan squares and a graph decomposition problem; (6) More results on the sequencing and 2-sequencing of groups; ADDITIONAL REMARKS; CHAPTER 4. LATIN SQUARES WITH AND WITHOUT SUBSQUARES OF PRESCRIBED TYPE; (1) Introduction
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(2) Without subsquares(3) With subsquares; (4) With subsquares and orthogonal; (5) Acknowledgement; ADDITIONAL REMARKS BY THE EDITORS; CHAPTER 5. RECURSIVE CONSTRUCTIONS OF MUTUALLY ORTHOGONAL LATIN SQUARES; (1) Introductory definitions; (2) Pairwise balanced designs - definitions; (3) Simple constructions for transversal designs; (3)* Examples; (4) Wilson's construction; (4)* Examples; (5) Weighting and holes; (5)* Examples; (6) Asymptotic results; (7) Table of values of N(v) up to v=200; ADDITIONAL REMARKS BY THE EDITORS; CHAPTER 6. r-ORTHOGONAL LATIN SQUARES
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(1) Some weaker modifications of the concept of orthogonality(2) r-Orthogonal latin squares and quasigroups; (3) Partial admissibility of quasigroups, its connection with r-orthogonality; (4) Spectra of partial orthogonality of latin squares (quasigroups); (5) Near-orthogonal and perpendicular latin squares; (6) r-Orthogonal sets of latin squares; (7) Applications of r-orthogonal latin squares and problems raised thereby; CHAPTER 7. LATIN SQUARES AND UNIVERSAL ALGEBRA; (1) Universal algebra preliminaries; (2) Varieties of latin squares; (3) Varieties of orthogonal latin squares
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(4) Euler's conjecture(5) Free algebras and orthogonal latin squares; CHAPTER 8. EMBEDDING THEOREMS FOR PARTIAL LATIN SQUARES; (1) Introduction; (2) Systems of distinct representatives; (3) The theorems of Ryser and Evans (on latin rectangles and squares); (4) Cruse's theorems (on commutative latin rectangles and squares); (5) Embedding idempotent latin squares; (6) Conjugate quasigroups and identities; (7) Embedding semisymmetric and totally symmetric quasigroups; (8) Embedding Mendelsohn and Steiner triple systems; (9) Summary of embedding theorems
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(10) The Evans' conjecture. (Smetaniuk's proof)
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English
Additional Edition:
ISBN 0-444-88899-3
Language:
English
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