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van Lint J.H., Wilson R.M. — Course in Combinatorics
van Lint J.H., Wilson R.M. — Course in Combinatorics

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Название: Course in Combinatorics

Авторы: van Lint J.H., Wilson R.M.

Аннотация:

A textbook for an upper level mathematics course that illustrates many links within combinatorics that seem unrelated, and surveys the field sufficiently to allow students to follow talks at conferences. A course in modern algebra is recommended but not required. The second edition adds material to the 1998 first, updates references, and corrects some minor errors.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1992

Количество страниц: 542

Добавлена в каталог: 05.03.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
(0, 1)-matrices      39 81ff 148ff
1-factor in a graph      476
1-factorization of a graph      476
1-skeleton of a polytope      424—425
15 schoolgirls problem      210
2-cell embedding of a graph      409 433ff
2-designs      196ff 277
3-claw      499
3-connected graph      422—424 433
36 officers problem      251
5-designs      195 212 219 222—223 225 492
6-designs      196
Absolute bound for strongly regular graphs      240 243
Acyclic edge      430
Acyclic orientations of a graph      405
Addressing problem      62ff
Adjacency matrix of a digraph      390
Adjacency matrix of a graph      233ff 391—402 449ff
Adjacency matrix of a multigraph      449
Adjacency matrix of a scheme      367
Adjacency matrix of a tournament      390
Adjacent vertices in a graph      4
Affine geometry      270
Affine hyperplane      184
Affine plane      199 243 254
Affine subspace      270
Affine translation plane      286
Algebraic methods      60 233 237
Alltop, W.O.      195 212
Alphabet of a code      214
Andre, D.      119 130
Andre, J.      286 290
Andre’s reflection principle      118
Antichain      42ff 293
Appel, K.      20 27 28 427 428 447
Arborescence      13 125
ARC      313—315 328
Arithmetic progression      26
Assmus — Mattson theorem      219
Assmus, E.F.      219 229
Associates in a scheme      365ff
Association matrices of a scheme      367ff
Association scheme      246 364ff
Atomic lattice      271
Augmenting path      54 see
Automorphism of a code      225 229
Automorphism of a graph      3 381 482 500
Automorphism of a map      441
Automorphism of a symmetric design      316 329ff 338
Automorphism of a tree      12
Axis of perspectivity      283
Baer subplane      225 317 353
Baer, R.      225
Baker, R.D.      267
Balanced incomplete block design (BIBD)      189ff
Balinski, M.      425 426
Ballot problem      130
Bannai, E.      372 389
Baranyai, Zs.      475 476 479
Baranyai’s theorem      475ff
Base blocks      208 211
Base of a Ferrers design      137
Bases in a combinatorial geometry      276ff
Batten, L.M.      290 328
Baumert, L.D.      177 186 354 498
Beineke, L.W.      248
Belevitch, V.      173 186 235
Bell numbers      105 107
Bermond, J.-C.      476
Bertrand, J.L.F.      130
Best, M.R.      180 186
Beth, T.      267
Bhattacharya, K.N.      211 212
Biggs, N.      401 427 447
Binary code      214 424
Binary Golay code      212 222—223 226 493
Binary relation on a set      365
Binary tree      119
Binet, A.      450
Bipartite graph      20 35 45 54 289 399
Biplane      237
Birkhoff, G.      40 41 92
Birkhoff’s theorem      40 53 92
Block design      189ff
Block graph of a design      236
Block of cheese      33
Blocking set in a projective plane      317
Blocks of an incidence structure      187
Blocksize of a t-design      188
Bollobas, B.      33
Bond of a graph      416ff
Bond-graph      411 416
Bondy, J.A.      9 481
Boolean algebra      269
Bose — Mesner algebra of a scheme      368ff 378 389
Bose — Mesner algebra of a strongly regular graph      234ff
Bose, R.C.      211 234 241 246 247 248 251 255 267 326 328 368
Bouwkamp, C.J.      460
Brandt, J.      164
Breadth-first search      17—18 66
Bregman, L.M.      82 89
Bridge      431
Bridges of Koenigsberg      6 7 10 47
Brooks, R.L.      20 27 28
Brooks’ theorem      20 27
Brouwer, A.E.      242 246 248 366 389 476 480
Bruck — Ryser — Chowla theorem      202 211 342 356
Bruck, R.H.      211 202 212 247 248 340 342 356
Buermann, H.      510
Burnside, W.      75
Burnside’s Lemma      75 330 463
Cameron, P.J.      228 229 246 247 248 492
Capacity of a cut      49ff
Capacity of an edge      49ff
Catalan numbers      116—121 130 145
Catalan, E.      116 130
Catherine the Great      251
Cauchy inequality      96
Cauchy — Binet theorem      450
Cauchy, A.L.      75 89 450
Cayley graph      445—447
Cayley, A.      11 18 446
Cayley’s Theorem      11ff 125 450
cell      142
Chain      42ff 272
Chakravarti, I.M.      328
Chandrasekharan, K.      146 202 212
Chang graphs      241 247
Chang, L.C.      241 247 248
CHARACTER      175 218 354
Chartrand, G.      406 414 426 433 447
Cheapest spanning tree      16 481
Chinese remainder theorem      260
Chowla, S.      202 211 212 267 268 342 356
Chromatic number      20 327 398 427 500
Chromatic polynomial      306 311 404
Chvatal, V.      55
Circle geometries      327
Circuits of a graph      416ff
Circular sequences      75—76 101
Claw      190 500
Claw bound      242—243
Clebsch graph      233 246 440 447 503
Clebsch, A.      233 246 440
Clique in a graph      241 393
Clique in a scheme      380
Closed path      5
Closed walk      5 410
Closure in a combinatorial geometry      274ff
Coboundary space of a digraph      454
Coboundary space of a graph      414
Coclique in a graph      392—393 397
Coclique in a scheme      380
Code      213ff 355ff
Code in a scheme      381
Code of a design      226—228 355ff
Code of a graph      414ff
Codewords      214
Coding theory      213—214 228—229 364
Coefficient      506
Cohen, A.M.      366 389
Cohen, G.D.      211 212
Coline      275
Collinear      242
Collineation of a projective plane      315
Colorings of graphs      20 306 427ff
Column of a Latin square      157
Columncomplete      170
Combinatorial design      313
Combinatorial geometry      269ff
Combinatorial proofs of identities      102—103 105 118 126 487
Cometric scheme      381
Complement of a design      192 221
Complement of a difference set      351
Complement of a graph      393 495
Complement of a symmetric design      360
Complement of an incidence structure      187
Complementing permutation      307
Complete bipartite graph      6 31 444
Complete cycle      57—60
Complete graph      3 11 20 22—23 25 27 29ff 63 189—190 390 436 441 444 450 476
Complete mapping of a group      265
Complete matching in a bipartite graph      35ff 45
Complete multipartite graph      30
Complete uniform hypergraph      479
Complexity of a graph      405 459
Component      5
Composition methods      255
Composition of a number      134 489
Conference matrix      173ff 205 235 360
Configuration counting series      467
Confoundable words      394
Conjugate of a partition      136 148
Conjugates of a Latin square      158
Connected combinatorial geometry      279 496
Connected graph      5—6 311
Connected strongly regular graph      231
Connectivity of a graph      406
Connor, W.S.      200 212 247 248
Conservation of flow      50
Contraction of edges      403ff
Convex combination of permutation matrices      40 92
Convex n-gon      26 119 126
Convex polytope      301 311 423
Conway, J.H.      188 493
Cost of an edge      16 49
Cotree      411
Counting in two ways      4 180 185 191 232
Covering in a poset      269 271 300
Covering radius      215 217
Crapo, H.      289 290 425 426 496
Crawley, P.      279 285 270 290
Cruse, A.      480
Cut in a transportation network      50
Cutoff      167
Cutset space of a graph      414
Cutsets of a graph      414ff
Cvetkovic, D.M.      397 401
Cycle index      463
Cycle space of a digraph      454
Cycle space of a graph      414
Cycles of a graph      415ff
Cycles of a permutation      104 107 463ff
Cyclic difference set      332ff 498
Cyclotomic scheme      367
d-code in a metric scheme      351
Da Silva, D.A.      77
de Beauregard Robinson, G.      145 146
De Bruijn graphs      56ff
De Bruijn sequences      56ff
De Bruijn — Erdoes theorem      188 391
de Bruijn, N.G.      44 48 56 60 61 188 212 391 471 474
De La Vallee-Poussin, C.J.      185
de Moivre, A.      89
de Montmort, P.R.      77
De Morgan, A.      427
Decode      182 184
Dedekind $\eta$-function      146
Dedekind, J.W.R.      146
Degree of a face      413
Degree of a vertex      4
Degrees of a scheme      365
Dehn, M.      460
Deletion of edges      403ff
Delsarte, p.      247 248 364 371 372 378 381 383 389
Delsarte’s inequalities      365 375 377
Dembowski, P.      290 328
Denes, J.      171
Denniston, R.H.F.      195 212 314 328
Depth of an orthogonal array      158
Depth-first search      17 18
Derangements      71 81 109 122
Derivation      126
Derived design      200
Desargues configuration      283
Desargues, G.      284 289
Desarguesian planes      285
Desargues’ theorem      284 287 288
Design of experiments      211
Design theory      187
Designs in a scheme      381
Determinant of the distance matrix      65
Difference methods      206 211 255 261ff 440
Difference set      329 330
Digraph      2
Dilworth, R.P.      42 48 279 285 270 290
Dilworth’s theorem      42 44 48
Dimension of a combinatorial geometry      274
Dirac, G.A.      32
Directed Eulerian circuit      14 56 60
Directed graph      2
Directed path      15
Discrepancy function      67
Distance between vertices      5
Distance in a code      214
Distance matrix of a graph      64—65
Distance regular graph      366
Distribution vector in a scheme      365 375—376
dodecahedron      8 434
Dominant eigenvalue      399
Doob, M.      401
Doubly stochastic matrix      40 86 89 91ff
Dowling, T.      306 307 312
Drawing of a graph      1 408
Dual arc in projective planes      314—315
Dual code      216
Dual graph      410ff
Dual of a symmetric design      199
Dual partial geometry      242
Dual poset      273
Duijvestijn, A.J.W.      456 460
Dulmage, A.L.      262 268
Echelon form      216 293—294
Edge colorings      22
Edges of a graph      1
Edmonds, J.      54 55 444 448
Egecioglu, 6.      14 18
Egoritsjev, G.P.      91
Eigenmatrices of a scheme      372
Eigenspaces      234 239 369
1 2 3 4
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