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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
(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 $3 \Times 3$ 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 $\phi$      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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