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| Sachkov V.N., Tarakanov V.E. — Combinatorics of Nonnegative Matrices |
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| Предметный указатель |
 -covering of a matrix 92
-depth of a matrix 90 91
Absorption index 240
Acyclic class 220
Acyclic matrix 221
Aperiodic class 220
Aperiodic matrix 221
Aperiodic vertex 220
Associated operator 214 232
Associated operator, nonsingular 240
Balanced incomplete block design 6
Basis ones 69
Basis set of positions 69
Bipartite graph 173
Boolean algebra 118 139
Boolean function 149
Boolean matrix 118
Canonical matrix of a Ryser class 47
Chain 215
Chainable matrix 166 184
Chainable matrix, minimal 186
Characteristic function 2
Circuit 215
Circuit diameter of a strong component 216
Circuit, elementary 215
Circulant 5 27
Circulant, primitive 29
Class property 218
Collinear elements 10
Column-composite class 63
Communicating vertices 217
Complemented lattice 139
Component of a digraph 216
Component of a digraph, strong 215
Component of a digraph, strong, nontransient 215
Component of a digraph, strong, q-universal 244
Component of a digraph, strong, transient 215
Composite class 63
Configuration 2
Configuration of subsets 2
Connected graph 185
Consistent system of equations 150
Convergence index 231 244
Convergent sequence 244
Cover rank 14 172
Cover rank, proper 172
Cover rank, strictly proper 172
Covering 171
Covering number 91 92
Covering problem 91
Covering, proper 171
Covering, strictly proper 171
CYCLE 186
Cyclic configuration 36
Cyclic matrix 5 221
Cyclic projective plane 37
Cyclotomic polynomial 40
Decomposition of a digraph into circuits 50
Degree of a vertex in a hypergraph 92
Depth of a matrix 91
Determinant of a matrix 11
Deterministic matrix 235
Diagonal 10 192
Diagonal matrix 161
Diagonal product 166
Diagonal, partial 10 192
Diagonal, positive 10
Diagonal, row 192
Diameter 228
Diameter of a component 216
Diameter of a strong component of a digraph 216
Difference set 36
Distributive lattice 139
Doubly stochastic configuration 4
Doubly stochastic matrix 13
Doubly stochastic model 166
Elementary class 63
Elementary matrix 207
Equivalent configurations 4
Essential vertex 217
Essentially nonsingular matrix 176
Essentially nonsingular matrix, strictly 177
Even graph 50
Exponent of a class of matrices 184
Exponent of a graph 120
Exponent of a matrix 119 224
Exponent of a tournament 228
Extremal matrix 88
Factorable matrix 199 208
Forbidden configuration 85
Free Boolean algebra 141
Frobenius function 221
Frobenius — Koenig theorem 12
g-circulant 27
g-circulant matrix 27
Graph 6
Graph configuration 6
Hypergraph 6 92
Incidence matrix 3
Incidence matrix, formal 181
Inconsistent system of equations 150
Indecomposable matrix 215 219 221
Independent generating system 141
Independent ones 69
INDEX 214
Index of a matrix 239
Index of a nonnegative matrix 230
Index of an associated operator 240
Inessential vertex 217
Interchange graph 51
| Interchange operation 48
Invariant 0-position 62
Invariant 1-position 62
Invariant one 62
Invariant set for a Ryser class 62
Invariant zero 62
Irreducible graph 173
Irreducible matrix 215 221
k-discordant permutations 129
Koenig Theorem 14
Koenig — Frobenius theorem 192
Kronecker product of matrices 29
Latin configuration 4
Latin rectangle 4
Latin square 5
Lattice 139
m-permutation 24
Markov chain 249 261
Markov chain, homogeneous 261
Markov chain, strongly ergodic 262
Markov chain, weakly ergodic 261
Maximal matrix 17
Minimal -covering 92
Minimal connected graph 168
Minimal covering 144
Monoid with unique cyclic decomposition 128
Monomial 208
Multigraph 6
Multiplicative rank 205
Multiplier of a difference set 37
Nearly decomposable matrix 168
Nearly partially decomposable matrix 168
Nonnegative matrix 2
Normal form of a matrix 215
Nullity 159 171
Nullity, proper 171
Oscillating sequence 244
Packing circuit number 51
Partially decomposable matrix 161 170
Path 185
Perfectly decomposable matrix 212
Period 231 244
Period of a circulant 29
Period of a class of vertices 220
Period of a vertex 219
Periodic matrix 221
Periodic sequence 244
Permanent of a matrix 11
Permanent, decomposition of 11
Permutation matrix 4
Permutation with restricted positions 127
Permutation with restricted positions, cyclic 129
Permutational automorphism 7
Permutationally equivalent matrices 4
Ph. Hall Theorem 15
Positive diagonal 166
Positively symmetric matrix 237
Prime matrix 199 208
Primitive graph 120
Primitive matrix 119 224
Problem on forbidden configurations 85
Pseudograph 6
Quasiconsistent system 150
r-indecomposable matrix 200
r-primitivity 214 250
r-primitivity, strong 214 256
r-regular hypergraph 92
Rank of a hypergraph 92
Reducible graph 174
Rook polynomial 129
Row-composite class 63
Ryser class 16
Ryser class, monotone 17
Saturation index 241
Schur function 11
Schur lemma 225
Scope 206
Semi-irreducible graph 173
Semi-totally indecomposable matrix 171
Smirnov sequence 124
Smirnov sequence, cyclic 126
Standard form of a matrix 97
Stochastic configuration 4
Strongly connected digraph 215
Structure 139
Structure matrix 17
Subconfiguration 85
Support of a matrix 2
Symmetric block design 36
t-covered element 146
t-minimal covering 145
t-quasiconsistent system 150
Term rank 10
Term rank, maximal 26
Totally indecomposable matrix 161 170
Tournament 213 227
Tournament, irreducible 227
Tournament, primitive 228
Tournament, reducible 227
Tournament, transitive 213 230
Transformation of a matrix 188
Transversal 10
Transversal number 92
Transversal number for a hypergraph 92
Undirected graph 6
Unimodal sequence 61
Vertex connectivity 54
Weak ergodicity theorem 252
Weakly totally indecomposable matrix 171
Weight function 2
Width of a matrix 91
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