Kolchin V.F. — Random Graphs :: Электронная библиотека попечительского совета мехмата МГУ

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Kolchin V.F. — Random Graphs

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Название: Random Graphs

Автор: Kolchin V.F.

Аннотация:

Results of research on classical combinatorial structures such as random graphs, permutations, and systems of random linear equations in finite fields.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1999

Количество страниц: 252

Добавлена в каталог: 23.11.2009

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Предметный указатель

Algorithm $A_{2}$       173
Characteristic function      8
Classical scheme of allocation      16
Complete description of distribution of the number of cycles      192
Connected component      23
Connectivity      22
Critical graph      91
Critical set      125
Decomposable property      23
Distribution function      2
Equations involving permutations      219
Equations of compound degree      235
Equations of prime degree      225
Factorial moment      3
Feedback point      124
Forest      21
Forest of nonrooted trees      30
Generalized scheme of allocation      14
Generating function      6
Graphs with components of two types      70
Homogeneous system of equations      125
Hypercycle      126
Independent critical sets      125
Inversion formula      10
Length of the maximum cycle      212
Limit distribution of the number of hypercycles      164
Linearly independent solutions      125
Local limit theorem      10
Mathematical expectation      3
Maximal span      9
Maximum number of independent critical sets      125 135
Maximum size of components      66
Maximum size of components of a random graph      84
Maximum size of trees in a random forest      48
Maximum size of trees in a random graph      83
Maximum size of trees in a random graph from $A_{n,T}$       71
Mean      3
Mean number of solutions in the equiprobable case      132
Method of coordinate testing      168
Multinomial distribution      15
Multiplicity of a vertex in a set of hyperedges      126
Nonequiprobable graph      109
Normal distribution      9
Number of components      107 144
Number of components in $\mathcal{U}_{n}$       65
Number of cycles in a random permutation      182 183
Number of cycles of length r in a random permutation      182
Number of forests      31
Number of linearly independent solutions      130
Number of nontrivial solutions      131

Number of trees of fixed sizes      71
Number of trees with r vertices      42
Number of unicyclic components      77 81
Number of unicyclic graphs      58
Number of vertices in the maximal unicyclic component      81
Number of vertices in unicyclic components      71 77
Order of random permutation      239
Order statistics      17
Partition      19
Permutations with restrictions on cycle lengths      192
Poisson distribution      6
probability      1
probability distribution      2
Probability of consistency      144
Probability of reconstruction of the true solution      166
Probability space      1
Problem of moments      4
Process of sequential growth of the number of rows      127
Random element      1
Random forest      21 30
Random graph corresponding to random permutation      181
Random graph of a random permutation      182
Random graphs with independent edges      100
Random matrices with independent elements      126
Random pairwise comparisons      164
Random partitions      30
Random permutation      28
Random variable      1
Rank of matrix      124
Rank of random sparse matrices      135
Reconstructing the true solution      165
Saddle-point method      7 221
Set of rooted trees      21
Shift register      123
Simple classification problem      122
Single-valued mapping      18
Statistical problem of testing the hypotheses $H_{0}$ and $H_{1}$       180
Subcritical graph      91
Summation of independent random variables in GF(2)      131
Supercritical graph      91
System of linear equations in GF(2)      122
System of random equations with distorted right-hand sides      180
System with at most two unknowns in each equation      156
Threshold property      156
Total number of components      24
Total number of critical sets      157
Total number of cycles      102 212
Total number of hypercycles      158
Unicyclic graph      58
Voting algorithm      165
Weak convergence      2

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