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Sachkov V.N., Tarakanov V.E. — Combinatorics of Nonnegative Matrices
Sachkov V.N., Tarakanov V.E. — Combinatorics of Nonnegative Matrices

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Название: Combinatorics of Nonnegative Matrices

Авторы: Sachkov V.N., Tarakanov V.E.

Аннотация:

Explores the relationship between nonnegative matrices and the various mathematical structures of combinatorics. The authors first study classes of nonnegative matrices of identical form and with identical numbers of positive elements in rows and columns, extremal combinatorial problems related to nonnegative matrices, and asymptotic methods. They then consider the integral properties of nonnegative matrices related to indecomposability and chainability, and analyze the behavior of powers of nonnegative matrices as the exponent grows to infinity. The original Russian version was published in 2000


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2002

Количество страниц: 269

Добавлена в каталог: 29.11.2009

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\alpha$-covering of a matrix      92
$\alpha$-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 $\alpha$-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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