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| Sachkov V.N. — Combinatorial methods in discrete mathematics |
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| Предметный указатель |
 -configuration 25
 -substitution 191
Abelian semigroup 7
Action from the left 213
Action from the right 214
Adjacency matrix 166
Adjacent edges 166
Alternating group 274
Antichain 47
Appell set 113
Arrangement 15
Arrangement with unlimited repetitions 16
ascent 127
Automaton graph 71
Bernoulli polynomial 113
Binary relation 3
Binary relation, composition of 216
Binomial coefficient 17
Block 25
Boolean operation 1
Cartesian product 2
Characteristic polynomial 14
Characteristic root 14
Combination 15
Combination with unlimited repetitions 17
Composition law 6
Composition law, outer 10
Configuration 15
contour 12 167
Contour, elementary 12
Convex hull 61
Convex linear combination 61
Convex poly tope 61
Correspondence, binary 3
Correspondence, functional 3
Covering 264
Covering, k-block 264
Covering, minimal 266
Critical subfamily 50
CYCLE 13 166 187
Cycle class 188
Cycle class, enumerator of 190
Cycle class, maximal 188
Cycle class, minimal 188
Cycle index 272
Cycle of length l 187
Cycle, decrement of 195
Cycle, independent 187
Cycle, length of 13
Cycle, simple 166
Cyclic group 7
Cyclic sequence 144
de Morgan number 115
Decomposition 8
Descent 128
Determinate automaton without input 71
Diagonal 3
Diagram 4
Digraph 4 11 166
Digraph, arc of 166
Digraph, strongly connected 167
Digraph, strongly connected component of 167
Direction of the steepest descent 159
Doubly stochastic matrix 58
Doubly stochastic matrix, multiple 58
EDGE 4 165
Edge, directed 11
Edge, multiple 167
Eigenvalue 14
Eigenvector 14
Elementary matrix 70
Enumerator 229
Enumerator in commutative asymmetric basis 229
Enumerator in non-commutative asymmetric n-basis 240
Enumerator in non-commutative symmetric n-basis 258
Enumerator of exponential type 241
Equivalence class 4
Equivalence relation 4
Euler identity 144
Eulerian number 128
Factor group 9
Factor set 4
Factorial, falling 110
Factorial, rising 110
Fibonacci numbers 77
Finite projective plane 36
Fixed point 11
Forest 166
Formal power series ring 105
Function 5
G-stabilizer 213
Galois number 134
Gaussian coefficient 133
General combinatorial scheme 211 223
General combinatorial scheme, particular case of 223
Generating function 103 107
Generating function, exponential 104
Generating series 107
Generator system 182
GH-equivalence 215
Graph 165
Graph, bicolorable 171
Graph, bipartite 171
Graph, colorable 171
Graph, connected 166
Graph, connected component of 12 166
Graph, labeled 167
Graph, partially labeled 167
Graph, Polya 181
Graph, regular 166
Graph, unlabeled 167
Group 7
Group with finite number of generators 182
Group, orbit of 274
Group, order of 7
Groupoid 7
H-stabilizer 215
Hadamard configuration 36
Hadamard matrix 32
Hadamard matrix, normalized form of 33
Height 12 197
Homomorphism 8
Hyperplane 61
Image 3
Incidence algebra 108 217
Incidence algebra, reduced 109
Incidence algebra, standard 109
Incidence coefficient 109
Incidence matrix 3 6 25
Incident edge 166
Incident vertices 166
INDEX 8
Injective function 290
Input alphabet 293
Integral domain 106
interval 60
Inverse element 7
inversion 126
Isomorphism 8
Latin rectangle 20
Latin rectangle, matrix of 20
Latin square 20
Latin square, based on a group 23
Latin square, matrix of 20
Latin square, normalized 21
Latin square, orthogonal 21
| Latin square, seminormalized 22
Loop 167
m-combination 17
m-permutation 16
M-permutation with unlimited repetitions 16
m-sample 223 282
m-sample in commutative asymmetric n-basis 223
m-sample in commutative symmetric n-basis 223
m-sample in non-commutative asymmetric n-basis 223
m-sample in non-commutative symmetric n-basis 223
Mapping, bijective 6
Mapping, discordant 19
Mapping, injective 6
Mapping, many-valued 5
Mapping, single-valued 5
Mapping, surjective 6
Matrix, completely irreducible 98
Matrix, decomposition of 58
Matrix, diagonal of 60
Matrix, Kronecker product of 34
Matrix, minimizing 98
Matrix, non-collinear elements of 60
Matrix, partially reducible 98
Menage problem 75
Moebius function 143 218
Monogenic group 7
Monoid 7
Multigraph 167
Multiplication of substitutions 12
Multiset 212
n-basis 223
Necklace 282
Neutral element 7
Noerlund relation 110
Normal matrix 27
Operation 6
Operation, associative 7
Operation, commutative 7
Operation, distributive 7
Orbit 187 274
Orbit, weight of 289
Order 5
Order, linear 5
Order, partial 4
Ordering, lexicographical 5
Output alphabet 293
Output function 294
p-simplex 63
P. Hall conditions 50
Partially ordered set 5
Partition 139
Partition of number 228
Partition, block of 2
Partition, conjugate 250
Path 11 166
Path, elementary 12
Path, length of 166
Path, simple 166
Permanent rank 80
Permanent, decomposition of, by Laplace formula 74
Permanent, decomposition of, with respect to element 74
Permanent, decomposition of, with respect to row 74
Permutation 15
Permutation matrix 6 13
Polynomial coefficients 18
POSET 5 217
Poset, locally finite 217
Poset, lower bound of 217
Poset, upper bound of 217
Power group 217
Power set 2
Preimage 3
Probabilistic automaton 68
Probabilistic automaton without output 69
Probabilistic transformer 72
Projection 3
Quasigroup 7
Rank, boundary 80
Rank, line 80
Residue class, left 8
Residue class, right 8
Restriction 6
Rhymed sequence 226
Ring 9
Scalar product 14 61
Segment 108
Semigroup 7
Semipermutation matrix 68
Set of states 293
Set, locally finite 108
Set, perfect difference 32
Space, basis of 10
Specification 211
Specification, primary 211 212
Specification, secondary 211 212
Stabilizer 275
Step of formalization 222
Stirling number of the first kind 116
Stirling number of the second kind 116
Stochastic matrix 70
Subgraph 166 167
Subgroup 8
Subgroup, invariant 8
Substitution 6
Substitution, cycle of 187
Substitution, cycle of length l of 187
Substitution, decrement of 195
Substitution, even 195
Substitution, k-regenerative 125
Substitution, non-regenerative 125
Substitution, odd 195
Substitution, orbit of 187
Substitution, transitivity set of 187
Symmetric element 7
Symmetric group 13
System of distinct representatives 49
System of representatives 222
System of representatives, common 56
Transformation 11
Transformation, degree of 11
Transition function 294
Transitivity domain 274
Transpositions of degree n 181
Transpositions, regular product of 183
Transpositions, regular set of 183
Transpositions, support of set of 183
Transversal 49
Transversal, common 56
TREE 166
Tree, bichromatic 185
Tree, root of 167
Tree, rooted 12 167
Tree, unrooted 167
Truncation 6
TYPE 109
Unit element 7
Unitary polynomial 146
Vandermonde relation 110
Vector 10
Vertex 4 11 165
Vertex, degree of 166
Vertex, distance between 166
Vertex, end 166 178
Vertex, isolated 166
Walk 167
Zeta function 143
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