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Laywine C.F., Mullen G.L. — Discrete mathematics using Latin squares
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Название: Discrete mathematics using Latin squares
Авторы: Laywine C.F., Mullen G.L.
Аннотация: 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 squares. Discrete Mathematics Using Latin Squares is the
only upper-level college textbook/professional reference that fully engages the subject and its many important applications. Mixing theoretical basics, such as the construction of orthogonal Latin squares, with numerous practical examples, proofs, and exercises, this text/reference offers an extensive and well-rounded treatment of the topic. Its flexible design encourages readers to group chapters according to their interests, whether they be purely mathematical or mostly applied. Other features include: An entirely new approach to discrete mathematics, from basic properties and generalizations to unusual applications 16 self-contained chapters that can be grouped for custom use Coverage of various uses of Latin squares, from computer systems to tennis and golf tournament design An extensive range of exercises, from routine problems to proofs of theorems Extended coverage of basic algebra in an appendix filled with corresponding material for further investigation. Written by two leading authorities who have published extensively in the field, Discrete Mathematics Using Latin Squares is an easy-to-use academic and professional reference.
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Рубрика: Математика /Алгебра /Комбинаторика /
Статус предметного указателя: Готов указатель с номерами страниц
ed2k: ed2k stats
Год издания: 1998
Количество страниц: 326
Добавлена в каталог: 11.03.2005
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Предметный указатель
Latin square(s), partial 14 15
Latin square(s), perfect 258 264
Latin square(s), perfect, and conflict-free access to parallel memories 264
Latin square(s), perfect, main subsquare 258
Latin square(s), r-orthogonal 257 264
Latin square(s), reduced 4 112 113 126
Latin square(s), row 97—100 285
Latin square(s), row complete 11 115 126
Latin square(s), self-orthogonal 33 38 39 282
Latin square(s), symmetric idempotent 13
Latin square(s), transversals of 36 37
Latin square(s), unipotent 112 113
Lawrence, K.M. 244 250 251 254
Laywine, C F. 27 37 39 45 51 61 62 70 71 146 152 164 169 170 173 174 253 254
Lenz, H. 165 172 173
Lewis, J.T. 226
Lidl, R. 228 234 239 240 269 273 278
Lindner, C.C. 124 128
Lipschutz, S. 278
Loops 97
MacNeish's conjecture 26 27 37
MacNeish, H.F. 26 27 37 40 58
MacWilhams. F.J. 205 225 227
Magic cube 291
Magic squares 175—181 290
Magic squares, 3-dimensional 180
Magic squares, 3-dimensional, perfect 180
Magic squares, addition-multiplication 179 180
Magic squares, applications of 175
Magic squares, defined 175
Magic squares, multiplicative properties 181
Magic squares, order 7
Mahalanabis, A. 244 250 254
Mandl, R. 18 37 40 263 265
Mavron, V.C. 173 174
McKay, B.D. 16 17 127 128
Mead, R. 204
Melencolia I 175 176
Melliar-Smith, P.M. 259 264 266
Menage numbers 86 90 91 93
Menage problem 86—89 93
Menage problem, enumeration of 3-row latin rectangles 93
Mendelsohn, E. 124 128
Mendelsohn, N.S. 124 128
Mersenne primes 291
Moebius inversion 93
MOFS see Mutually orthogonal frequency squares
MOHC see Mutually orthogonal hypercubes
MOLS see Mutually orthogonal latin squares
Monte Carlo methods 253
Montgomery, D.C. 204
Moore, E.H. 20 38 40
MOPLS see Mutually orthogonal partial latin squares
Moschopoulos, E. 175
Moser, L.E. 259 264 266
Mullen, G.L. 27 37—40 45 48 51 62 70 71 89 93 101 104 146 147 151 152 169 174 216 217 226 227 244 248—251 253 254 278
Mullin, R.C. 171 173
Multiplication (Cayley) table 95 103
Mutually orthogonal frequency squares (MOFS) 64—70 284 288
Mutually orthogonal frequency squares (MOFS), complete set 64
Mutually orthogonal frequency squares (MOFS), construction by substitution 66—70
Mutually orthogonal frequency squares (MOFS), nonconstant frequency 70
Mutually orthogonal frequency squares (MOFS), polynomial construction 64—66
Mutually orthogonal hypercubes (MOHC) 43—62 247—254 288 289 294
Mutually orthogonal hypercubes (MOHC) and affine designs 153—173
Mutually orthogonal hypercubes (MOHC), blocks 153 171 172
Mutually orthogonal hypercubes (MOHC), complete set 51
Mutually orthogonal hypercubes (MOHC), composition 153
Mutually orthogonal hypercubes (MOHC), defined 44
Mutually orthogonal hypercubes (MOHC), higher orthogonality 250—252
Mutually orthogonal hypercubes (MOHC), Hoehler orthogonality 61
Mutually orthogonal hypercubes (MOHC), MacNeish construction 57 58
Mutually orthogonal hypercubes (MOHC), order 6 59
Mutually orthogonal hypercubes (MOHC), polynomial construction 47—51 248
Mutually orthogonal hypercubes (MOHC), recursive construction 51—57 61 249 250
Mutually orthogonal hypercubes (MOHC), type 44
Mutually orthogonal Latin squares (MOLS) 18—39 280—282 285 292 294
Mutually orthogonal latin squares (MOLS) and Kronecker product 280 281
Mutually orthogonal latin squares (MOLS), applications 18 37
Mutually orthogonal latin squares (MOLS), complete set 20
Mutually orthogonal latin squares (MOLS), deficiency of a set 33
Mutually orthogonal latin squares (MOLS), defined 19
Mutually orthogonal latin squares (MOLS), Desarguesian construction 21 22
Mutually orthogonal latin squares (MOLS), Desarguesian set 22 35
Mutually orthogonal latin squares (MOLS), isomorpbic sets 22 34
Mutually orthogonal latin squares (MOLS), maximum number 19
Mutually orthogonal latin squares (MOLS), nondesarguesian 146 147
Mutually orthogonal latin squares (MOLS), nonisomorpbic sets 22
Mutually orthogonal latin squares (MOLS), nonprime power sets 23 24
Mutually orthogonal latin squares (MOLS), polynomial representation 20 21
Mutually orthogonal latin squares (MOLS), power set of 35 36
Mutually orthogonal latin squares (MOLS), prime power sets of 20 21
Mutually orthogonal latin squares (MOLS), sets of nonisomorphk 280
Mutually orthogonal partial latin squares (MOPLS) 255—257 264
Mutually orthogonal partial latin squares (MOPLS), application to computer databases 256 257
Mutually orthogonal partial latin squares (MOPLS), p-compatible 255
Nets 293—295
Niederreiter, H. 228 234 239 240 242—244 249 250 253 254 269 273 278
Niven, I. 269 278
Norton, D.A. 104 105
Numerical integration 241 242 253
One-way analysis of variance (ANOVA) 188 201
Order, definitions of 102
Orthogonal array(s) 31 32 36 37 197 246 247 280 281 294
Orthogonal array(s), equivalent objects 31 32
Orthogonal array(s), generalized 251
Orthogonal hypercubes see Mutually orthogonal hypercubes
Orthogonal latin square graph (OLSG) 123—126
Orthogonality, Hoehler's definition of 61
Pairwise orthogonal squares 19
Pandiagonal latin squares (Knut — Vik designs) 179
Parker, E T. 8 17 26 37 39 40 101
Partial latin square(s) 230 239
Permutation cube(s) 43 223 224—226
Permutation cube(s), reduced 224 225
Permutation(s), theory of 95 96
Perspective triangles 143—146
Pilz, G. 269 278
Piper, F.C. 152
Plane(s), affine and projective 131—152
Plane(s), desarguesian 172
Plane(s), Euclidean 131 135 136 143
Plane(s), Hall 146 147 151 172
Pless, V. 225 227
Poch, G. 263—265
Polynomials, irreducible 272 273 277 278 280
Posner, E.C. 213 216 226
Preece, D.A. 264 265
Prime power conjecture 38 152
Prime power conjecture, Hoehler's partial resolution of for hypercubes 61 62
Primes, Fermat 291
Primes, Menenne 291
Primitive element 274 277 291
Principle of inclusion-exclusion 75—93
Principle of inclusion-exclusion, defined 75 76
Probert, R.L. 264—266
Projective planes, axioms defining 138 139
Projective planes, desarguesian 143—146 151
Projective planes, Fano 150
Projective planes, Hall 146 147 151
Projective planes, Hughes 151
Projective planes, incidence matrix 149 150
Projective planes, incidence matrix, and duality principle 150
Projective planes, nondesarguesian 146—150
Projective planes, order of 139
Projective planes, points at infinity 139 140
Quad-groups 97
Quadrangle criterion 97 104
Quasi-Monte Carlo methods 253
Raghavarao, D. 45 62 64 70 170 173
Retkin, H. 102 104 105
Ring, commutative 270
Riordan, J. 90 93
Rivest, R.L. 237—240
Rogoyski, E. 16 17 127 128
Rook polynomials 80—86 92 285
Rook polynomials, defined 80 81
Room squares 182—187 238 262
Room squares and duplicate bridge tournaments 182 183 186
Room squares, defined 182
Room squares, Howell master sheets 182
Room, T.G. 182—187
Rota. G.-C. 93
Row effects 190
Row-latin square(s) 97—100
Row-latin square(s), latin power set 99
Row-latin square(s), orthogonal 98 99
Row-latin square(s), power set 99
Ryser. H.J. 38 39 93 152
Salzburg, P.M. 263 265
Sandier, R. 152
Sarvate, D.G. 239 240
Schmid, W.C. 250 251 254
Schulz, R.-H. 263—265
Seberry, J. 239 240
Seiden, E. 45 62—64 70 170 173
Shamir, A. 237—240
Shiue, P.J.-S. 146 147 152
Shrikhande, S.S. 8 17 26 33 37—40 101 172—174
Simons, G.J. 230 239 240
Simpson rule 241
Singleton bound 212 221
Siu, M.-K. 96 104 105
Sloane, N.J.A. 205 225 244 254
Smetaniuk, B. 15—17 230 239 240
Smith, P. 58 62
Sphere-packing (Hamming) bound 211 224
Stinson, D.R. 8 17 37 40 117 128 263—265
Straus, E.G. 58 62
Street, A.P. 30 31 37 40 46 62 114 128
Street, D.J. 30 31 37 40 46 62 114 128
Suchower, S.J. 70 71 101 104 216 217 226 227
Swiercz, S. 38 39
Symmetric designs 155
Tarry, G. 7 8 23 37
Tay.T.-S. 257 264—266
Thiel, L. 22 38 39 146 151 152
Thompson, A.C. 181
Three-orthogonality 229 243 251
Tillson, T.W. 117 128
Tismeneteky, M. 159 173
Transversal design(s) 27—32 37
Trapezoidal rule 241
Two-way analysis of variance 189
Uniform pseudorandom numbers 242
Valeric M. 259 264 266
van Lint, J.H. 39 40
van Tilborg, H.C.A. 228 239 240
Vaughan, H.E. 109 128
Vector spaces 274—278
Vector spaces and error-corrrecting codes 276 277
Vector spaces, addition of vectors 274
Vector spaces, examples of 275 276
Vector spaces, finite-dimensional 276
Vector spaces, finite-dimensional, dimension of 276
Vector spaces, scalar multiplication 274
Vector spaces, sets of vectors 276
Vector spaces, sets of vectors, linear combination 276
Vector spaces, sets of vectors, linearly dependent 276 277
Vector spaces, sets of vectors, linearly independent 276 277
Vector spaces, sets of vectors, spanning 276
Vector spaces, subspaces 276—277
Wallis, W.D. 172 174 186 187
Wan, D. 146 147 152
Weber, R.E. 226 227
Whittle, G. 27 37 39 45 51 62 248 249 253 254
Williams, A.W. 264—266
Williams, E.J. 116 128
Wilson's problem 39
Wilson, R.M. 39 40
Wolk, B. 124 128
Yamamoto, K 91 93
Yates, F. 204
Zuckerman, H.S. 269 278
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