Combinatorics: Set Systems, Hypergraphs, Families of Vectors, and Combinatorial ProbabilityCambridge University Press, 31. 7. 1986 - Počet stran: 177 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. |
Obsah
1 Notation | 1 |
2 Representing Sets | 4 |
3 Sperner Systems | 10 |
4 The LittlewoodOfford Problem | 17 |
5 Shadows | 23 |
6 Random Sets | 35 |
7 Intersecting Hypergraphs | 45 |
8 The Turán Problem | 53 |
13 Intersecting Families | 95 |
14 Factorizing Complete Hypergraphs | 105 |
15 Weakly Saturated Hypergraphs | 116 |
16 Isoperimetric Problems | 122 |
17 The Trace of a Set System | 131 |
18 Partitioning Sets of Vectors | 135 |
19 The Four Functions Theorem | 143 |
20 Infinite Ramsey Theory | 155 |
9 Saturated Hypergraphs | 61 |
10 WellSeparated Systems | 71 |
11 Helly Families | 82 |
12 Hypergraphs with a given number of Disjoint Edges | 87 |
| 168 | |
| 176 | |
Další vydání - Zobrazit všechny
Combinatorics: Set Systems, Hypergraphs, Families of Vectors, and ... Béla Bollobás Náhled není k dispozici. - 1986 |
Běžně se vyskytující výrazy a sousloví
A E A A₁ A₂ AC X(r assertion assume B₁ b₂ best possible Bollobás colex order colour Combinatorial Theory completely Ramsey contains Corollary Daykin decreasing Deduce define disjoint elements equality holds Erdős Erdős-Ko-Rado theorem ex(n F₁ FC P(X finite sets Frankl Furthermore graph of order H-family Hadamard matrix Helly families Hence hypergraph implies induction hypothesis infinite subsets integer intersecting family k-colouring Katona Kleitman Kruskal-Katona theorem l-intersecting r-graph l-set lattice Lemma Let F LYM inequality m₁ Math matroid monotone increasing monotone increasing property natural number non-empty Note number of edges open set pairs poset precisely problem proof of Theorem property Q r-graph G r-sets r+s)-saturated random graph rank function real numbers result satisfying sequence set system Show Sperner family Sperner system Sperner's theorem subgraph Suppose symmetric chains system F threshold function topology triples trivial V₁ vectors vertices