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| Авторизация |
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| Ruskey F. — Combinatorial generation |
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| Предметный указатель |
A-order 107
Alphabet 11
Alternating permutation 111
Anchor 44
Antichain 19
Antimatroid 20 206 241
Antimatroid, basic words 20
Antipodal chain 191
APPEND 12
Arboricity 247
AVL tree 108
B-order 107
B-tree 86 108
B-tree, generating all 86—89
Backtracking, non-recursive algorithm 43 44
Backtracking, recursive algorithm 43
Backtracking, tree 43
Bag 15
Basic word graph 206
Bell number 17 35 89 90 93 109 159
BEST (Backtracking Ensuring Success at Terminals) 8 9 47
Bicentral tree 83
Binary tree 74 112
Binary tree, complete 102
Binary tree, Gray code 138 142 175
Binary tree, rotation 142
Binary tree, unordered 112
Binary trees, random generation of 252
Binomial coefficient 13
bitstring 11
Bracelet 232
Buckyball 204
Burnside’s Lemma 32 215
Campanology 189 205
CAT (Constant Amortized Time) 8 9
Catalan number 21 36 74 146
Catalan numbers 21
Cayley graph 33 189
Cayley graph over Abelian group 199
Center 83
Centroid 83
Chain 19
Change-ringing 189
Chinese Rings 178
CLIQUE 28 246 247
Closeness relation 116
Cluster 125
Co-lexicographic order 55
Colex (or RL) Superiority Principle 59
Comb 134
Combination 226
Combination of a multiset 71
Combination, Gray code 185
Combination, random 249
Combinations, Gray code 125
Combinatorial Gray code 116
Combinatorial Gray code, cyclic 116
composition 13 106 149
Composition with restricted parts 71
Composition, Gray code for 149—153
Concatenate 12
Concave 35
conjugate 16 109
Conjugate of numerical partition 37
Constant time initialization 34
Context-free language 232 252
Contingency table 71 110
Cover relation 19
Coxeter graph 195
Cubic graph 178 241
Cut 246
Cutset 246
CYCLE 246
Cycle lemma 107 252
de Bruijn, cycle 232
De Bruijn, graph 220
De Bruijn, sequence 220
De Bruijn, torus 232
Degree of a vertex 26
Degree sequence 110
Depth-first numbering 29
Depth-first search 29 209
Depth-first-search 243
Derangement 14 35 106 181 252
Digraph, connected 27
Digraph, strongly connected 27
Digraph, tournament 28
Direct algorithm 121
Distributive lattice 203
Dominating property 74
Dominoe 229
Dominoes 207
Euler pentagonal number theorem 37
Eulerian number 15
Eulerian, cycle 208 210
Eulerian, graph 208
Extension 19
Extension-rotation algorithm 176—178
extent 189 204
Ferrer’s diagram 16
Fibonacci number 33
Free tree 78 82 83 112
Free tree, generating all 82—86
Free tree, random generation of 252
Function 12
Function, bijection 12
Function, injective 12
Function, surjective 12
Graph 26
Graph, 1-Hamiltonian 205
Graph, acyclic 26
Graph, acyclic orientation 27 186 205
Graph, adjacency lists 29
Graph, adjacency matrix 28
Graph, arboricity of 247
Graph, automorphism group of 31
Graph, automorphism of 26
Graph, bipartite 27 240 241
Graph, Cayley 53
Graph, clique 28
Graph, coloring 28 52
Graph, complete ( ) 27
Graph, complete bipartite ( ) 27
Graph, connected 26
Graph, connected component 29
Graph, cube of 27 204 206
Graph, cubic 26 178 240
Graph, directed Cayley 33
Graph, generating non-isomorphic 236—238
Graph, grid 204
Graph, Hamilton-connected 28
Graph, Hamilton-laceable 28
Graph, Hamiltonian 28 37
Graph, hypercube ( ) 27
Graph, hypo-Hamiltonian 28
Graph, independent set 28
Graph, pancyclic 28
Graph, planar 247
Graph, prism of 27 205
Graph, product of 27
Graph, random 252
Graph, regular 26
Graph, shuffle-exchange 206
Graph, spanning subgraph of 28
Graph, square of 27 204—206
Graph, subgraph of 26
Graph, undirected Cayley 33
Graph, unicyclic 24 241
Graph, vertex cover 28
Graph, vertex-transitive 26 31
| Graphical partitions 110
Gray code for binary trees 175
Gray code for combinations 125 185
Gray code for multiset permutations 146
Gray code, binary reflected (BRGC) 116 178 229
Gray code, binary tree 138 142
Gray code, composition 149
Gray code, monotone 190
Gray code, numerical partition 153
Gray code, set partition 159
Gray code, uniform 122
Gray code, well-formed parenthesis 139
Greedoid 241
Group 26 30
Group, abelian 31 199
Group, action 31
Group, cyclic 30 232
Group, dihedral 30 232
Group, generating set for 33
Group, hypo-octohedral 31
Group, order of 30
Group, order of an element in 30
Group, subgroup 30
Group, symmetric 30 31
Group, transitive 31
Hamilton cycle 28 53
Hamilton laceable 179
Hamilton path 28 204
Hamiltonian cycle, algorithm for 176—178
Hamming distance 11 178
Hasse diagram 19
Height-balanced (AVL) tree 113
Hexomino 51
Hypercube 114 202 203 210
Hypercube () 27 117
Ideal 20
Ideal, generating all 101—103
In-tree 23 208
Independent set 28
Independent set, maximal 246
Index of a permutation 14
Indirect algorithm 121
inversion 14 106
Inversion string 111
Inversion, string 68 106 111
Inversion, table 111
Inversion, vector 111
Involution 15 106 111 230
Knight’s tour 52
Labelled trees 78
Latin rectangle 106 106
Lattice 19 241
Lattice, distributive 20 203
Lexicographic order 55
Linear algorithm 9
Linear extension 19 27 52 110 113
Linear extension, generating all 99—101
Linear extension, Gray code for 165—174
Linear feedback shift register (LFSR) 228—229
LIST 11
List, append 12
List, concatenation of 12
List, interface between 12
List, prepend 12
Log-concave 35
Logarithmically concave 73
Loopless 5
Loopless algorithm 121
Lyndon, factorization 222
Lyndon, word 185 214 216 217 220 227 230 231 233
Lyndon, word, random 250
Magic square 110
Matching, perfect 247
Matrix tree theorem 194
Matroid 247
Matroid, listing bases of 247
Maximal independent set 247
Memoryless 5 56 67
Middle two levels problem 182
Moebius, function 215
Moebius, inversion 17 215
Monotone runs 106
Multinomial coefficient 15
Multiplicity representation 94 109 238
Multiset 15
Multiset permutations 185
Multiset, combinations of 71
Multiset, specification of 68
Murasaki diagram iii
N-queens problem 41
Natural representation 94 109
Necklace 213 216 217
Necklace of a string 222
Necklace, factorization 222
Necklace, random 250
NUMBER 11
Numerical partition 93 113
Numerical partition into distinct parts 109
Numerical partition into odd parts 109
Numerical partition, conjugate of 37
Numerical partition, Gray code 153
Numerical partition, random 251
Ordered forest 107
Ordered tree 112
Ordered tree, degree of a node 20
Orthogonality relation 107
Out-tree 23 208
Parity difference 14 181
Partially ordered set 19
Partite set 27
Partition 16
Partition, binary 109
Partition, numerical 16 238
Partition, numerical, conjugate of 16
Partition, part of 93
Partition, set 17 225
Partition, set, block of 17
Partition, set, with given block sizes 164
Partitions, graphical 110
Pascal’s triangle 13
Pendant vertex 26 154
Pentomino 44
Permutation 14 111
Permutation of a multiset, random 250
Permutation, alternating, Gray code for 164
Permutation, cycle 106
Permutation, cycle notation 14
Permutation, cycle representation 34
Permutation, cycles in 14
Permutation, derangement 14 35 106 181 252
Permutation, even 14
Permutation, index of 14
Permutation, inverse 34 35
Permutation, inverse of 14
Permutation, inversion 14 35 106
Permutation, inversion string of 68 111
Permutation, involution 15 35 106
Permutation, k-permutation 15
Permutation, odd 14
Permutation, one-line notation 14
Permutation, parity of 14
Permutation, random 249
Permutation, rosemary 111
Permutation, run 15
Permutation, sign 34
Permutation, sign of 14
Permutation, transposition 14
Permutation, up-down 15 106
Permutohedron 19
PET 61
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