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Sachkov V.N. — Probabilistic Methods In Combinatorial Analysis
Sachkov V.N. — Probabilistic Methods In Combinatorial Analysis

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Название: Probabilistic Methods In Combinatorial Analysis

Автор: Sachkov V.N.

Аннотация:

This work explores the role of probabilistic methods for solving combinatorial problems. The subjects studied are nonnegative matrices, partitions and mappings of finite sets, with special emphasis on permutations and graphs, and equivalence classes specified on sequences of finite length consisting of elements of partially ordered sets; these define the probabilistic setting of Sachkov's general combinatorial scheme. The author pays special attention to using probabilistic methods to obtain asymptotic formulae that are difficult to derive using combinatorial methods. This important book describes many ideas not previously available in English and will be of interest to graduate students and professionals in mathematics and probability theory.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1997

Количество страниц: 246

Добавлена в каталог: 20.11.2009

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$A\Lambda$-partition      133
$\Lambda$-permutation      147
$\sigma$-algebra      3
A-forest      226
Absolute moment      8
Aleksandrov, A.D.      49
Asymptotically normal sequence      22
Bender, E.      32
Bernoulli numbers      29
Bernoulli trials      11
Bessel function      15
Binomial distribution      11
Bonferroni inequalities      14
Boole inequality      2
Cauchy integral formula      10
Central limit theorem      21 22
Central limit theorem for sums of independent random variables      22
Central limit theorem for triangular arrays      23
Central moment      8
Characteristic function      18
Characteristic function of a lattice distribution      20
Characteristic function of a normal distribution      20
Characteristic function of a Poisson distribution      19
Characteristic function of a uniform distribution      18 19
Chebyshev inequality      8
Complement of an event      2
Complementary event      2
Complete set of events      2
Complexity of a matrix      169
Conditional probability      4
Configuration      82
Connected component      186
Continuity theorem      21
Continuity theorem for generating functions      18
Continuous random variable      5
Continuous random vector      5
Curtiss' theorem      25
Cutting number of a vertex      183
Cyclic elements      175
Decrement of a permutation      152
Degree of a vertex      174
Density of a distribution      5 6
Density of a normal distribution      5
Discrete random variable      3
Discrete space      2
Disjoint permutations      50
Distance between vertices      180
distribution      4
Distribution function      4
Distribution law      3
Distribution, binomial      11
Distribution, hypergeometric      12
Distribution, lattice      19
Distribution, limiting      18
Distribution, nondegenerate normal      6
Distribution, normal      5
Distribution, Pascal      11
Distribution, Poisson      12
Distribution, standard normal      5
Dominant function of a polynomial      38
Double generating function      32
Egorychev, G.P.      49
Euler numbers      30 31
Event      2
Event, certain      2
Event, complementary      2
Event, elementary      2
Event, impossible      2
Event, opposite      2
Events, difference of      2
Events, disjoint      2
Events, mutually exclusive      2
Events, mutually independent      4
Events, product of      2
Events, sum of      2
Evolution of a random graph      191
Expectation      see "Mathematical expectation"
Factor of the first degree      191
Falikman, D.I.      49
Forest      172
Frechet formulae      16
Generating function      10
Generating function of Bernoulli numbers      29
Generating function of binomial moments      10
Generating function of factorial moments      10
Generating function of moments      10
Generating function of Morgan numbers      34
GH-equivalence      82
Global degree of a graph      192
Graph of a mapping      175
Graph, balanced      192
Graph, connected      186
Graph, Polya      191
Hall conditions      48
Height of a mapping      206
Height of a tree      174
Hypergeometric distribution      12
Incidence matrix      48
Inclusion-Exclusion Principle      13
Independent random variables      6
Inequality, Bonferroni      14
Inequality, Boole      3
Inequality, Chebyshev      8
Integral limit theorem      22—24
Inverse image of an element      204
Inversion formula for characteristic functions      19
Inversion formula for probability distributions      13
Inversion in a random permutation      29
Koenig — Frobenius theorem      49
Labeled elements of a basis      106
Laplace formula      17
Lattice      20
Length of a path      174
Levy — Cramer theorem      21
Limiting distribution      18
Lindeberg condition      23
Local limit theorem      24
London, D.      49
Lyapunov theorem      23
Mass of a vertex      182
Matching problem      13 108
Mathematical expectation      7
Matrix, double stochastic      165
Matrix, incidence      48
Matrix, permutation      49 50
Matrix, stochastic      165
Mean      7
Mean value      7
Measurable space      3
Moment generating function of a discrete random variable      10
Moment generating function of a normal distribution      25
Moment generating function, in the general case      25
Moment of the kth order      8
Moment of the kth order, absolute      8
Moment of the kth order, binomial      8
Moment of the kth order, central      8
Moment of the kth order, factorial      8
Morgan numbers      34
Ordered sample      159
Pascal distribution      11
Permanent      49
Permanents of random matrices      55
Permutation      50
Permutation with congruent cycles      150
Permutation with cycles of even length      151
Permutation with cycles of odd length      151
Permutation, cycles in      152
Permutation, disjoint      50
Permutation, even      152
Permutation, odd      152
Poisson distribution      12
Poisson sequence      23
Primary specification      82
probability      3
probability distribution      see "Distribution"
Probability of an event      2
Probability space      4
Probability, conditional      4
Probleme des rencontres      see "Matching problem"
Prufer, H.      173
Random graph      185
Random variable      3 4
Random variable, continuous      5
Random variable, discrete      3
Random variable, integer-valued      9
Random variable, lattice      19
Random variable, n-dimensional      5
Random walk around a tree      183
Regular threshold function of a property      192
Residue      78
Rise in a permutation      30
Root of a tree      172
Rooted tree      172
Rooted tree, recursive      172 185
Rooted tree, unlabelled      172
Secondary specification      82
Sequence, asymptotically normal      22
Sequence, Poisson      23
Set of images      204
Skeleton of a mapping      206
Space of elementary events      2
Standard normal distribution      5
Stieltjes integral      7
Stirling expansion      41
Stirling numbers of the first kind      9
Stirling numbers of the second kind      9
Threshold distribution function      192
Threshold function      192
Threshold function, regular      192
Total probability formula      4
Transversal      48
Transversal, conditions of nonexistence      62
Transversal, limit theorems for      60 61
TREE      172
Tree, labeled      172
Unlabeled tree      172 184
Unrooted labeled tree      172
Valency of a vertex      173
Van der Waerden conjecture      49
Variance      8
Weak convergence      21
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