LEADER 05164nam 2200625 450 001 9910827538203321 005 20200520144314.0 010 $a0-444-63558-0 010 $a0-444-63555-6 035 $a(CKB)3710000000453346 035 $a(EBL)2121478 035 $a(OCoLC)916952508 035 $a(SSID)ssj0001565636 035 $a(PQKBManifestationID)16208673 035 $a(PQKBTitleCode)TC0001565636 035 $a(PQKBWorkID)14834193 035 $a(PQKB)10036394 035 $a(MiAaPQ)EBC2121478 035 $a(Au-PeEL)EBL2121478 035 $a(CaPaEBR)ebr11084772 035 $a(CaONFJC)MIL822748 035 $a(PPN)19867869X 035 $a(EXLCZ)993710000000453346 100 $a20150815h20152015 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aLatin squares and their applications /$fJ. De?nes, A. D. Keedwell 205 $aSecond edition. 210 1$aAmsterdam, [Netherlands] :$cAcademic Press,$d2015. 210 4$dİ2015 215 $a1 online resource (439 p.) 300 $aDescription based upon print version of record 320 $aIncludes bibliographical references and index. 327 $a""Front Cover""; ""Latin Squares and their Applications""; ""Copyright""; ""Foreword to the First Edition""; ""Contents""; ""Preface to the First Edition""; ""Acknowledgements (First Edition)""; ""Preface to the Second Edition""; ""Chapter 1: Elementary Properties""; ""1.1 The Multiplication Table of a Quasigroup""; ""1.2 The Cayley Table of a Group""; ""1.3 Isotopy""; ""1.4 Conjugacy and Parastrophy""; ""1.5 Transversals and Complete Mappings""; ""1.6 Latin Subsquares and Subquasigroups""; ""Chapter 2: Special Types of Latin Square""; ""2.1 Quasigroup Identities and Latin Squares"" 327 $a""2.2 Quasigroups of Some Special Types and the Concept of Generalized Associativity""""2.3 Triple Systems and Quasigroups""; ""2.4 Group-Based Latin Squares and Nuclei of Loops""; ""2.5 Transversals in Group-Based Latin Squares""; ""2.6 Complete Latin Squares""; ""Chapter 3: Partial Latin Squares and Partial Transversals""; ""3.1 Latin Rectangles and Row Latin Squares""; ""3.2 Critical Sets and Sudoku Puzzles""; ""3.3 Fuchsa??? Problems""; ""3.4 Incomplete Latin Squares and Partial Quasigroups""; ""3.5 Partial Transversals and Generalized Transversals"" 327 $a""Chapter 4: Classification and Enumeration of Latin Squares and Latin Rectangles""""4.1 The Autotopism Group of a Quasigroup""; ""4.2 Classification of Latin Squares""; ""4.3 History of the Classification and Enumeration of Latin Squares""; ""4.4 Enumeration of Latin Rectangles""; ""4.5 Enumeration of Transversals""; ""4.6 Enumeration of Subsquares""; ""Chapter 5: The Concept of Orthogonality""; ""5.1 Existence Questions for Incomplete Sets of Orthogonal Latin Squares""; ""5.2 Complete Sets of Orthogonal Latin Squares and Projective Planes""; ""5.3 Sets of MOLS of Maximum and Minimum Size"" 327 $a""5.4 Orthogonal Quasigroups, Qroupoids and Triple Systems""""5.5 Self-Orthogonal and Other Parastrophic Orthogonal Latin Squares and Quasigroups""; ""5.6 Orthogonality in Other Structures Related to Latin Squares""; ""Chapter 6: Connections Between Latin Squares and Magic Squares""; ""6.1 Diagonal (or Magic) Latin Squares""; ""6.2 Construction of Magic Squares with the Aid of Orthogonal Latin Squares.""; ""6.3 Additional Results on Magic Squares""; ""6.4 Room Squares: Their Construction and Uses"" 327 $a""Chapter 7: Constructions of Orthogonal Latin Squares Which Involve Rearrangement of Rows and Columns""""7.1 Generalized Bose Construction: Constructions Based on Abelian Groups""; ""7.2 The Automorphism Method of H.B. Mann""; ""7.3 The Construction of Pairs of Orthogonal Latin Squares of Order Ten""; ""7.4 The Column Method""; ""7.5 The Diagonal Method""; ""7.6 Left Neofields and Orthomorphisms of Groups""; ""Chapter 8: Connections with Geometry and Graph Theory""; ""8.1 Quasigroups and 3-Nets""; ""8.2 Orthogonal Latin Squares, k-Nets and Introduction of Co-ordinates"" 327 $a""8.3 Latin Squares and Graphs"" 330 $aLatin 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 606 $aMagic squares 615 0$aMagic squares. 676 $a512.9/25 700 $aDe?nes$b J.$01213825 702 $aKeedwell$b A. D. 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910827538203321 996 $aLatin squares and their applications$92803231 997 $aUNINA