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Laywine C.F., Mullen G.L. — Discrete mathematics using Latin squares
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Название: Discrete mathematics using Latin squaresАвторы: 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
Язык: Рубрика: Математика /Алгебра /Комбинаторика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 1998Количество страниц: 326Добавлена в каталог: 11.03.2005Операции: Положить на полку |
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(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 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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