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Bollobás B. — Combinatorics: Set Systems, Hypergraphs, Families of Vectors and Combinatorial Probability
Bollobás B. — Combinatorics: Set Systems, Hypergraphs, Families of Vectors and Combinatorial Probability

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Название: Combinatorics: Set Systems, Hypergraphs, Families of Vectors and Combinatorial Probability

Автор: Bollobás B.

Аннотация:

Combinatorics is a book whose main theme is the study of subsets of a finite set. It gives a thorough grounding in the theories of set systems and hypergraphs, while providing an introduction to matroids, designs, combinatorial probability and Ramsey theory for infinite sets. The gems of the theory are emphasized: beautiful results with elegant proofs. The book developed from a course at Louisiana State University and combines a careful presentation with the informal style of those lectures. It should be an ideal text for senior undergraduates and beginning graduates.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1986

Количество страниц: 182

Добавлена в каталог: 23.04.2010

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
${h}_{k}$ family      83
(k,l)-intersecting family      87
ACCEPT      161
Adjacent      2
Almost constant sequence      111
Almost every      36
Almost no      36
Almost regular hypergraph      112
Almost surely      36
Antichain      14
Array      107
arrow notation      132
Baire property      164
Ball      103
Bernoulli random variable      50
Bipartite graph      6
Boundary      122
CEILING      3
Centre      103
Chain      14
Classical topology      160
Colex order      24
Colexicographic order      24
Colour      156
Colouring      155 160
Common transversal      142
Compatible permutation      66
Complete r-graph      54
Compressed set system      28
Compression operator      28
Connected graph      15
Cover      2
Covering graph      2
Critical set system      65
cube      3
Degree      81 112
Density of hypergraph      54
Diameter      102
Disconnected graph      15
Distance      3
Distance between set systems      126
Distributive lattice      145
Down-set      147
Dual chain      68
EDGE      2
Edge graph      2
Edge-boundary      123
Ellentuck topology      160
Embedding      120
Exterior algebra      117
Extremal hypergraph      53
Extremal problem      53
Extremal set system      53
Factor      106 112
Factorization      106 112
Falling factorial      3
Family      2
Family fixed by k vertices      87
Family fixed by l-subsets      88
Family of subsets      2
Fisher's Inequality      79
Fixed by an l-set      47
Flexible embedding      120
FLOOR      3
Forbidden subgraph      53 54
Forbidden subgraph problem      53
Graph      2
Ground set      1 136
Hadamard matrix      74
Hall's Condition      6
Hamming ball      126
Hamming distance      3
Helly family      83
Hyperedge      1
Ideal      16 36
incident      2
Independent set      136
Intersecting family      45
Intersecting hypergraph      45
Intersecting Sperner system      96
interval      95
Isomorphic      2
Isoperimetric inequality      123
Joined      2
k-dimensional array      107
k-independent set      139
Kirkman triple system      113
Kirkman's Fifteen Schoolgirls Problem      105
l-intersecting set system      47
Lattice      1
Left compressed      28 99
Level set      14
Lex order      24
Lexicographic order      24
Linear graph      2
Log-supermodular function      148
Lower shadow      23
LYM inequality      11
Matching      6
Mathias topology      160
Matroid      136
Meagre set      164
Monochromatic set      155 157
Monotone decreasing property      35 36
Monotone decreasing set system      16
Monotone increasing property      35 36
Monotone increasing set system      16
Monotone property      35
Multiple cover      121
n-dimensional cube      3
Non-trivial property      37
Nowhere dense set      163
Order      2
Own subset      84
Paley matrix      75
Partially ordered set      1
POSET      1
Power set      1
Probability space      35
Problem of Turan      54
Property      35
Property of set systems      55
r-graph      1
r-uniform hypergraph      1
RADIUS      103
Random graph      35
Random k-set      36
Rank formula      140
Rank function      14 136
Ranked poset      14
Regular hypergraph      112
Regularly connected poset      14
Reject      161
Representing sets      65
Restriction      131
Rigid embedding      120
Saturated hypergraph      61
Set of distinct representatives      5
Set system      1
Shadow      23
SIZE      2
Sperner family      10
Sperner system      10
Steiner triple system      113
Submodular      138
Sylvester's problem      105
Symmetric difference      2
Threshold function      36
topology      160
Trace      131
Trace number      131
Transversal      5 135
Transversal matroid      136
Transversal number      65
TREE      8
Unrelated chains      68
Up-set      147
Upper shadow      23
Vertex      2
Vertex-boundary      123
Weakly saturated hypergraph      116
Weight      11 62
Weight of a chain      68
Well-separated system      73
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