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| Tucker A. — Applied Combinatorics |
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| Предметный указатель |
a-z cut 138
Addition principle 172
Adjacency matrix 49 110
Adjacent vertices 3
Adler, I. 315
Aho, A. 49 132
Ahuja, R. 166 167
Algorithmic proof procedure 413
Ancestor in a tree 94 426
Anderson, I. 429
Appel, K 36 76 88 92
Arrangement(s) 180 423
Arrangement(s) with repetition 196
Art Gallery Problem 87
Ascent in permutation 346
Assignment problem 126
Augmenting flow algorithm 144
Augmenting matching algorithm 157
Automorphism of graph 54
Backtracking in graph 103 426
Balanced tree 96 426
Ball, W 403
Barnette, D. 92
Behzad, M. 429
Berge, C. 277 399 403 429 430
Berlekamp, E. 403
Berman, G. 429
Bernoulli, Jacob 231
Bernoulli, Jacques 231 417
Biggs, N 48 92 429
Binomial coefficient 181 213 423
Binomial coefficient, generalized 310
Binomial identities 213
Binomial theorem 214
Bipartite graph 4 31 75 156 423
Bipartite graph, deficiency 165
Birthday paradox 192
Bishops, dominating 16
Blockwalking 216
Boat crossing puzzle 109
Bogart, K. 429
Bondy, J. 48 92 429
Boole, G. 408
Boolean algebra 406
Bouton, C. 403
Boyer, C. 409
Branch-and-bound search 118
Breadth-first search 104 426
Bridge in a graph 52
Bridge probabilities 203
Brook’s Theorem 88
Brualdi, R. 427
Bubble sort 127
Buck, R. 188 231
Burnside’s Lemma 361
Bussey, W. 413
C(n,r) 180
Capacity of cut 139
Capacity of edge 138
Capobianco, M. 429
Cardano, B. 417
Catalan number 311
Cayley, A. 48 99 132
Center of a tree 101
Chain in network 143
Characteristic equation 297 308
Characteristic sequence of a tree 109
Chessboard, generalized 339
Chromatic number 77 423
Chromatic polynomial 83 91 186 284
Circle-chord method 37
Circuit, in graph 4 423
CLIQUE 54
Closure in group 355
Coalition voting 188
Cohen, D 419 429
Cohen, J. 48
Coin balancing 98
Color critical graph 83 90
Coloring a graph 77 331 423
Combination 180 423
Combination, algorithm for 226
Committee scheduling 8 79
Complement of chessboard 347
Complement of graph 23 83 90 424
Complement of set 406
Complete graph 21 29 423
Component of graph 46 424
Configuration in graph 39
Conjugate of Ferrers graph 263
Conjunction of propositions 407
Connected graph 41 424
Connected graph, algorithm for connectedness 110
Conway, J. 403
Cormen, T. 295 315
Coxeter, H. 403
Crossing number 45
Cut in network 138
Cut-set 53 154
Cycle in a graph 53 57 424
Cycle in permutation 354
Cycle index 368
Cycle structure representation 367
David, F. 231 418
de Moivre, A. 276 315 348
De Morgan, A. 408 413
Deadheading edge 59
DeCarteblanche, F. 403
Deficiency of bipartite graph 165
Degree of a region 42
Degree of a vertex 20
Degree of a vertex in-degree and out-degree 23
Deo, N. 231 232
Depth-first search 103 426
Derangement 330 424
Descendant in a tree 94
Dictionary search 6 97
Difference equation 287 315
Difference of sets 406
Digital sum 398
Dijkstra, O. 133
Direct sum of graph 397
Dirichlet drawer principle 420
Disjunction of propositions 408
distribution 202 424
Divide-and-conquer relations 293
DNA model 9 198
Dominating set 54
Dual graph 36
Durfee square 265
Edge chromatic number 88
Edge cover 7 16 158 424
Edge in graph 3
Edge in graph, directed edge 3
Elements of set 405
Equitable coloring 83
Equivalence class 352
Equivalence relation 352
Euler cycle 57 72 91 424
Euler trail 61
Euler, L 41 48 57 277
Euler’s constant e 188 268 330
Euler’s formula for graphs 41 236
Event of outcomes 416
Event of outcomes, compound event 416
Event of outcomes, elementary event 416
Expected value of random variable 259
Experiment 416
Factor in graph 383
Factor in graph, labeled factor 383
| Feller, W. 276 277
Fermat, P. 231 417
Ferrers diagram 262
fibonacci 315
Fibonacci numbers 276 281 308 315
Fibonacci relation 281 308 299 315
Fleury’s algorithm 64
Flow chart 14
Flow in network 138
Flow in network in a planar network 155
Flow in network, dynamic flow 149
Flow in network, value of flow 139
Floyd’s algorithm for shortest paths 135
Ford, L. 166 167
Forest of trees 101
Four color problem 36 76 88 92
Fourier transform 276
Fryer, K. 429
Fulkerson, D. 166 167
Functional equation 306
Galileo 417
Garbage collection 81
Generating functions 243 306 424
Generating functions, exponential 267
Generating functions, ordinary 243
Generators of group 358
Gould, R 430
Graham, R. 419 429
Graph 3
Graph, directed graph 3 19 387 424
Graver, J. 430
Gray code 71
Group of symmetries 356
Grundy function 392 398
Grundy, P. 403
Guy, R. 403
Haken, W 36 76 88 92
Hall, M 430
Hall’s marriage theorem 159
Halmos, P. 409
Hamilton, W. 92
Hamiltonian circuit and path 65 91 118 424
Harary, F. 49 380 430
Heap 129
Heap sort 129
Height of tree 96 129
Hillier, F. 167
Hit polynomial 336
Hopcroft, J. 49 132
Hypercube 72
Identical Objects Rule 417
Identity of group 355
Inclusion-exclusion formula 325
Independent set 77 425
Induction 411
Initial conditions in recurrence relation 279
Instant Insanity puzzle 381
Integer solution of equation 205 245 328
Interest problems 283
Internal vertex 94
Intersection of sets 406
Interval graph 9 10 27 28 80 91 425
Interval graph, unit-interval graph 17
Inverse in a group 355
Isolated vertices 22
Isomers of organic compounds 358
Isomorphism of graphs 20 425
Jackson, B. 429
Kayles game 395
Kernel of game 390
Kiefer, J. 315
Kirchhoff, G 48 132
Knight’s tour 63
Knuth, D. 413 429
Konig, D. 48
Konigsberg bridges 57
Konig’s Infinity Lemma 387
Kruskal’s minimal spanning tree algorithm 112
Laplace transform 276
Laplace, S. 277 415 417
Lawler, E. 132
Leaves of tree 94 426
Lehmer, D. 231 232
Leibnitz, G. 231
Leiserson, C. 295 315
Length of path or circuit 31
Lenstra, J. 132
Lesniak — Foster, L. 429
Level numbers in a progressively finite, graph 391
Level numbers in tree 94 426
Lexicographic order 224
Lieberman, G. 167
Line graph 47 54 63 76
Linear program 166
Linked list 50
Liu, C 429
Lloyd, E. 48 92 429
Lovasz, L. 429
Lucas, E. 132
MacMahon, P. 277
Magnanti, T. 167
Map coloring 36 425
Matching in graph 4 156 425
Matching in graph, maximal 156
Matching in graph, X-matching 156
Matching network 157
Maurolycus 413
Max Flow-Min Cut Theorem 147
Maze searching 104
Member of set 405
Menage 347
Merge sort 128
Minimal spanning tree 111
Molluzzo, J. 429
Moments of random variable 259
Montmort, P. 348
Mounting climbing 29
Multigraph 57 425
Multiplication principle 172
Multiplication, fast 295
Murty, U. 48 92 429
Negation of proposition 408
Network 133 425
Network flow 138
Nievergelt, J. 231 232
Nijenhuis, A. 430
Nim game 396
Nonconsecutive arrangements 207
Nonplanar graph 46
Ore, O. 430
Organic compounds 358
Orlin, J. 167
O’Rourke, J. 87 92
P(n,r) 180
Palmer, E. 380
Parent in a tree 94 427
Parenthesization 310
Parsing 18
Partitions 260 425
Partitions of integer 260
Partitions, ordered 265
Partitions, self-conjugate 265
Pascal, B 231 413 415 417
Pascal’s triangle 216 231 413
Patashnik, O. 429
Path in graph 4 425
Pattern inventory 351 374
Peacock, G. 408
Permutation 180 425
Permutation, algorithm 225
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