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Laywine C.F., Mullen G.L. — Discrete mathematics using Latin squares
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.


Язык: en

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

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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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