Book contents
- Frontmatter
- Contents
- Preface
- List of contributors
- Acknowlegements
- Generating expanders from two permutations
- Sum-free subsets
- Is there a different proof of the Erdős-Rado theorem?
- Almost collinear triples among N points on the plane
- Hamilton cycles in random graphs of minimal degree at least k
- The circumference of a graph with a given minimal degree
- On arithmetic progressions in sums of sets of integers
- On graphs not containing prescribed induced subgraphs
- Partitions sans petits sommants
- A compact sequential space
- The critical parameter for connectedness of some random graphs
- Multiplicative functions on arithmetic progressions: III. The large moduli
- Locally finite groups of permutations of ℕ acting on l∞
- Hypergraph games and the chromatic number
- On arithmetic graphs associated with integral domains
- On the number of certain subgraphs of graphs without large cliques and independent subsets
- Sets of multiples of Behrend sequences
- A functional equation arising from mortality tables
- The differences between consecutive primes, IV
- On the cofinality of countable products of cardinal numbers
- On σ-centered posets
- A Galvin–Hajnal conjecture on uncountably chromatic graphs
- Necessary conditions for mean convergence of Hermite–Fejér interpolation
- On the Erdős–Fuchs theorems
- A tournament which is not finitely representable
- On the volume of the spheres covered by a random walk
- Special Lucas sequences, including the Fibonacci sequence, modulo a prime
- A remark on heights of subspaces
- Incompactness for chromatic numbers of graphs
- Graphs with no unfriendly partitions
- On the greatest prime factor of an arithmetical progression
- The probabilistic lens: Sperner, Turan and Bregman revisited
- On the mean convergence of derivatives of Lagrange interpolation
- Sur une question d'Erdős et Schinzel
- Large α-preserving sets in infinite α-connected graphs
- Some recent results on interpolation
- Partitioning the quadruples of topological spaces
- Some of my favourite unsolved problems
Preface
Published online by Cambridge University Press: 05 March 2012
- Frontmatter
- Contents
- Preface
- List of contributors
- Acknowlegements
- Generating expanders from two permutations
- Sum-free subsets
- Is there a different proof of the Erdős-Rado theorem?
- Almost collinear triples among N points on the plane
- Hamilton cycles in random graphs of minimal degree at least k
- The circumference of a graph with a given minimal degree
- On arithmetic progressions in sums of sets of integers
- On graphs not containing prescribed induced subgraphs
- Partitions sans petits sommants
- A compact sequential space
- The critical parameter for connectedness of some random graphs
- Multiplicative functions on arithmetic progressions: III. The large moduli
- Locally finite groups of permutations of ℕ acting on l∞
- Hypergraph games and the chromatic number
- On arithmetic graphs associated with integral domains
- On the number of certain subgraphs of graphs without large cliques and independent subsets
- Sets of multiples of Behrend sequences
- A functional equation arising from mortality tables
- The differences between consecutive primes, IV
- On the cofinality of countable products of cardinal numbers
- On σ-centered posets
- A Galvin–Hajnal conjecture on uncountably chromatic graphs
- Necessary conditions for mean convergence of Hermite–Fejér interpolation
- On the Erdős–Fuchs theorems
- A tournament which is not finitely representable
- On the volume of the spheres covered by a random walk
- Special Lucas sequences, including the Fibonacci sequence, modulo a prime
- A remark on heights of subspaces
- Incompactness for chromatic numbers of graphs
- Graphs with no unfriendly partitions
- On the greatest prime factor of an arithmetical progression
- The probabilistic lens: Sperner, Turan and Bregman revisited
- On the mean convergence of derivatives of Lagrange interpolation
- Sur une question d'Erdős et Schinzel
- Large α-preserving sets in infinite α-connected graphs
- Some recent results on interpolation
- Partitioning the quadruples of topological spaces
- Some of my favourite unsolved problems
Summary
This volume is dedicated to Paul Erdős, who has profoundly influenced mathematics this century. He has worked in number theory, complex analysis, probability theory, geometry, interpolation theory, algebra, set theory and, perhaps above all, in combinatorics. His theorems and conjectures have had a decisive impact. In particular, he, more than anybody else, is the founder of modern combinatorics, he pioneered probabilistic number theory, he is the master of random methods in analysis and combinatorics, and he has created the fields of Ramsey theory and the partition calculus of set theory.
Paul Erdős is the consummate problem solver: his hallmark is the succinct and clever argument, often leading to a solution from ‘the book’. He loves areas of mathematics which do not require an excessive amount of technical knowledge but give scope for ingenuity and surprise. The mathematics of Paul Erdos is the mathematics of beauty and insight.
One of the most attractive ways in which Paul Erdős has influenced mathematics is through a host of stimulating problems and conjectures, to many of which he has attached money prizes, in accordance with their notoriety. He often says that he could not pay up if all his problems were solved at once, but neither could the strongest bank if all its customers withdrew their money at the same time. And the latter is far more likely.
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- A Tribute to Paul Erdos , pp. ix - xPublisher: Cambridge University PressPrint publication year: 1990