Электронная библиотека Попечительского совета механико-математического факультета Московского государственного университета
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
(t,m,s)-Nets 241-254
(t,m,s)-Nets and coding theory 250
(t,m,s)-Nets and error-correcting codes 250 254
(t,m,s)-Nets and MOLS 244-250 253 254
1-factorization and 1-factor 107 126 286 287
Abbadi, A.E. 256 264 265
Abdel-Ghaffar, K.A.S. 256 257 264 265
Abel, R.J. 27 37 39
Adleman, L. 237-240
Affine geometries 161-166 171 173
Affine geometries, k-flats defined 161
Affine plant(s) 68-70
Affine plant(s), algebraic derivation 133-136
Affine plant(s), axioms, defining 131
Affine plant(s), desarguesian 143-146
Affine plant(s), nondesarguesian 146-150
Affine plant(s), order of finite 132
Agrippa, C. 175
Albert, A.A. 152
Algebraic background 269-277
Alspach, B. 180 181
Andrews, G.E. 269 278
Andrews, W.S. 179-181
anova 188 201.
Appd, H. 106 128
Archdeacon, D.S. 117 128
Arkin, J. 58 62
Axial classes 289
Background, algebraic 269-277
Bain, L. 188 204
Balanced incomplete block design 153 154
Ball, R. 179 181
Batten, L.M. 145 152
Behzad, M. 106 128
Belyavskaya, G.B. 257 264 265
Berge, C. 93
Beth, T. 165 172 173
Bipartite graph 287
Blake, I.F. 171 173
Bloch, N.J. 104
Bose 1938 equivalence 137 152
Bose, R.C. 8 13 17 20 26 37-39 70 101 137 152 158 169 173 226
Brack, R.H. 33 38 39 123 128 152
Brayton, R.K. 33 38-39
Brock (geometric) nets 247
Brock - Ryser theorem 152
Brouwer, A.E. 27 31 37 39 213 215 219 220 226
Brouwer. table from 213 215 219 220 226
Bryant, V. 109 128
Bye-boards 182
Casanova, and magic squares 176
Cayley (multiplication) table 95 103
Cayley theorem 96
Cayley, A. 96
Characterizing graphs with Hamilton cycles, problem of 106
Chartrand, G. 106 128
Childs, L. 269 278
Classes, axial 289
Clayman, A.T. 244 254
Code(s) from MOFS 215 226
Code(s) from MOLS 209-213
Code(s), and latin squares 205-226
Code(s), binary 205
Code(s), constant weight 217 218
Code(s), error-correcting 123 205-226
Code(s), from orthogonal hypercubes 216
Code(s), Golomb - Posner MDS 213 216 226
Code(s), linear 206
Code(s), linear, nonlinear 208
Code(s), linear, rate of 208
Code(s), maximum distance separable (MDS), defined 212 213
Code(s), optimal 213-221
Code(s), protective 219
Code(s), q-ary 205
Code(s), repetition, of length it 209 210
Code(s), ternary 205
Code(s), two weight 219
Code(s), weight (wt) 207
Cohen, D. 117 128
Colboutn, C.J. 27 37 39 152 255 258-262 264 265
Column effects 190
Commutative ring 270
Cooper, J. 239
Coppersmith, D. 33 38 39
Craig, A.T. 188 204
Critical set(s) 231 238 239 293
Critical set(s) and latin square 293
Critical set(s), minimal 231 238 239
Cryptology and latin squares 228-239
Cryptology and latin squares, ciphertexts 228
Cryptology and latin squares, cryptology, cryptography, and cryptoanalysis defined 228
Cryptology and latin squares, enciphering and deciphering 228
Cryptology and latin squares, secret sharing schemes 230-233
Cryptology and latin squares, secret sharing schemes, multilevel 232
Cryptology and latin squares, secret sharing schemes, shadows of secret key 230
Cryptology and latin squares, secret sharing schemes, shares of secret key 230
Dean, R.A. 104
Deficiency of a set of MOLS 33 122
Dembowtki, P. 152
Denes, J. 8 16 17 22 23 33 36-39 43 62 70 97 101 102 104 105 116 117 128 146 152 175 179-181 184-186 223 226 247 253 254 257 263-265
Derangement 78
Desargues configuration 143-146
Desargues configuration, affine formulation 146
Desargues configuration, defined 143
Desargues theorem 144 145
Desarguesian plane(s) 172
Desarguesian set of MOLS 22 35
Desarguesian set of MOLS, construction of 21 22
Designs, affine resolvable 155 171-173
Designs, balanced incomplete block 153-155
Designs, resolvable 155
Designs, symmetric 155
Designs, transversal 27-32 37
Diffie, W. 234 235 239
Digital signature 237
Diirer, Melencolia I engraving 175 176
Dinitz, J.H. 27 37 39 117 128 152 186 187 255 260-262 264 265
Discordant permutation 77
Discrete logarithm cryptosystems 234-239
Discrete logarithm cryptosystems, no-key 236 237
Discrete logarithm cryptosystems, public-key 237 238
Discrete logarithm cryptosystems, RSA (Rivest, Shamir, and Adleman) 237-240
Discrete logarithm cryptosystems, RSA (Rivest, Shamir, and Adleman), and Euler's function 237 271
Discrete logarithm cryptosystems, three pas system 236 237
Discrete logarithm problem 103 234 239
Division algorithm 269
Donovan, D. 239
Dougherty, S.T. 5 37 39
Du, B. 179 181
Ecker, A. 263-265
Elementary intervals 242 243
Engdhardt, M. 188 204
Erickson, D.L. 259 264 265
Error-correcting codes See Code(s) error-correcting
Etzion, T. 117 128
Euclidean plane(s) 131 135 136 143
Euler 36-officer problem 5-8 11 23 58 64 67 101 104 122 127 188
Euler bound 58-60
Euler circuit 119 120
Euler conjecture 8 23 26 27 37 58 101 104
Euler solution of Koenigsberg bridge problem 106 127
Euler, L. 5-8 11 23 26 27 37 39 58-60 101 104 106 127 128
Evans, T. 16 17
Fennat last theorem 106
Fennat primes 291
Fields and irreducible polynomials 272 273 277 278 280
fields, defined 270
Fields, finite 271 278.
Fields, Galois 273
Fields, properties of 274
Finite field 20 21 270-274 278
Finite field, primitive dements 274 277 291
Finizio, N.J. 226
Four color problem 106 126
Fractional replication plane(s) 226
Fraleigh, J.B. 269 278
Frequency square(s) 63-70
Frequency square(s), constant frequency 64
Frequency square(s), defined 63
Frequency square(s), nonconstant frequency 70
Frequency square(s), orthogonal sets of 63 64
Freund, J.E. 188 189 193 204
Frolov, M. 97 104 105
Gallian, J.A. 269 278
Galois field 273
Gardiner, M. 181
Generalized orthogonal array 251
Generator matrices 214-217 292
Geometric (Brock) nets 247
Geometric hypercubes, defined 163
Golf design 13
Golomb.S.W. 213 216 226
Graphs (and latin squares) 106-128
Graphs (and latin squares), adjacency matrix 112
Graphs (and latin squares), bipartite 107 126
Graphs (and latin squares), edges 106
Graphs (and latin squares), l-factori(zation) 107 126 286 287
Graphs (and latin squares), monochromatic 1-factor 107
Graphs (and latin squares), net 122 126
Graphs (and latin squares), pseudo-net 122
Graphs (and latin squares), regular 121
Graphs (and latin squares), strongly regular 121-123
Graphs (and latin squares), vertices 106
Grosswald, E. 269 278
Groups (and latin squares) 94-104
Groups (and latin squares), abelian 94
Groups (and latin squares), associative 94
Groups (and latin squares), commutative 94
Groups (and latin squares), cyclic 94
Groups (and latin squares), defined 94
Groups (and latin squares), examples of 94
Groups (and latin squares), finite 94
Groups (and latin squares), generator 94
Groups (and latin squares), identity element 94
Groups (and latin squares), inverse element 94
Groups (and latin squares), order n 94
Groups (and latin squares), properties of 94
Haken, W. 106 128
Hall marriage theorem 108 109 287
Hall plane(s) 146 147 151 172
Hall, M. 146 151 152
Hall, P. 109 128
Halmos, P.R. 109 128
Hamilton circuit(s) 118 119 126 287
Hamilton cycles, characterizing graphs with 106
Hamilton, J.R. 89 93
Hamiltonian path 115 116 126 287
Hamming (sphere-packing) bound 211 224
Hamming distance 206 226 257
Hamming, R.W. 206 226-227
Hansen, T. 273 278
Hedayat, A. 45 62-64 70 170 173
Heinrich, K. 180 181 258 264 265
Hellman, M.E. 234 235 239
Herstein, I.N. 96 104 105 269 278
Hill, R. 205 209 225 227
Hinkelmann, K. 199 204
Hoehler definition of orthogonality 61
Hoehler, P. 61 62
Hoffman, A.J. 33 38 39
Hogg, R.V. 188 204
Homer, W.W. 179 181
Howell master sheets 182. See also Room squares
Hughes polynomials 151 152
Hughes, D.R. 151 152
Hungerford, T.W. 104 105 269 278
Hypercube(s), algorithm for construction from latin squares 294
Hypercube(s), d-dimensional 43
Hypercube(s), from latin squares 294
Hypercube(s), geometric defined 163
Hypercube(s), Hoehler's definition of 61
Hypercube(s), latin 43 44
Hypercube(s), nonlatin 44
Hyperplanes 171-173
Hyperrectangles 70
Integers, congruent modulo n 269
Integers, ring of, modulo n 270
Intervals, elementary 242 243
Irreducible polynomials 272 273 277 278 280
Jungnickel, D. 165 172 173
Kaplansky, I. 93
Karteszi, F. 152
Keedwell, A.D. 8 16 17 22 23 33 36-39 43 62 70 97 104 116 117 128 146 152 175 179-181 184-186 223 226 247 253 254 257 263-265
Kemptborne, O. 199 204
Kim, K. 258 264 265
Kimberiey, M E. 173
Kishen, K. 43 48 62
Knut - Vik designs (pandiagonal latin squares) 179
Koblitz, N. 239 240
Koch, J. 106 128
Koenigsberg bridge problem 106 127
Kolesova, G. 22 39 146 151 152
Kronecker product and hypercubes 57 58
Kronecker product and MOLS 23-27 124 125 280-282
Kumar, V.K.P. 258 264 265
Lagrange interpolation formula 20 274 296
Lagrange interpolation formula and polynomial representation 274
Lagrange theorem 38
Lam, C.W.R. 22 38 39 146 151 152
Lancaster, P. 159 173
Latin rectangle 15 93
Latin rectangle, first row 75 90 91
Latin rectangle, second row 75 84 85
Latin rectangle, third row 85-90
Latin square(s) and geometry 13 14
Latin square(s) and graphs 106-128
Latin square(s) and groups 94-104
Latin square(s) and linear algebra 14
Latin square(s), and statistics 188-204
Latin square(s), applications 255-265
Latin square(s), applications, (r, s)-conflict free and parallel array access problem 258 259 264
Latin square(s), applications, agricultural experiments 9-11
Latin square(s), applications, authentication schemes 263 264
Latin square(s), applications, check character systems 263 264
Latin square(s), applications, classic squares and broadcast squares 259 260 264
Latin square(s), applications, code design 11 12 101 102 228-239 263-265
Latin square(s), applications, committee formation 8 9
Latin square(s), applications, compiler testing 263 265
Latin square(s), applications, cryptography 101 102 205-226 228-239 263-265
Latin square(s), applications, drug test design 11
Latin square(s), applications, experimental design 9-11 264
Latin square(s), applications, golf design 13 262
Latin square(s), applications, hash functions 263 264
Latin square(s), applications, network testing systems 263-265
Latin square(s), applications, tomography 263 265
Latin square(s), applications, tournament design 12 13 260-262
Latin square(s), column complete 115
Latin square(s), complete 115
Latin square(s), defined 3
Latin square(s), diagonal 36
Latin square(s), disjoint transversals 33 36
Latin square(s), generalized 257 264
Latin square(s), idempotent 33 34 36 123 124 282
Latin square(s), introduction to 3-17
Latin square(s), nearly consecutive symbols 263
Latin square(s), order n 279
Latin square(s), orthogonal 5-9 281
Latin square(s), orthogonal mates 32 33 36
Latin square(s), orthogonal sets 18 36 37
Latin square(s), orthogonal, pair of 21
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