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Mathematics of Paul Erdos / [edited by] Ronald L. Graham, Jaroslav Nesetril and Steve Butler.

Contributor(s): Material type: TextTextPublication details: New York : Springer, 2013.Edition: 2nd edDescription: 2v. : ill. ; 24 cmISBN:
  • 9781461472575 (v. 1 : acidfree paper)
  • 9781461472537 (v. 2 : acidfree paper)
Subject(s): DDC classification:
  • 510 23 G741
Contents:
Vol. 1. : Paul Erdos: Life and Work -- Paul Erdoos Magic -- Part I Early Days -- Introduction -- Some of My Favorite Problems and Results -- 3 Encounters with Paul Erdös -- 4 Did Erdös Save Western Civilization? -- Integers Uniquely Represented by Certain Ternary Forms -- Did Erdös Save Western Civilization? -- Encounters with Paul Erdös -- On Cubic Graphs of Girth at Least Five -- Part II Number Theory -- Introduction -- Cross-disjoint Pairs of Clouds in the Interval Lattice -- Classical Results on Primitive and Recent Results on Cross-Primitive Sequences -- Dense Difference Sets and their Combinatorial Structure -- Integer Sets Containing No Solution to x+y=3z -- On Primes Recognizable in Deterministic Polynomial Time -- Ballot Numbers, Alternating Products, and the Erdös-Heilbronn Conjecture -- On Landau's Function g(n) -- On Divisibility Properties on Sequences of Integers -- On Additive Representation Functions -- Arithmetical Properties of Polynomials -- Some Methods of Erdös Applied to Finite Arithmetic Progressions -- Sur La Non-Dérivabilité de Fonctions Périodiques Associées à Certaines Formules Sommatoires -- 1105: First Steps in a Mysterious Quest -- Part III Randomness and Applications -- Introduction -- Games, Randomness, and Algorithms -- The Origins of the Theory of Random Graphs -- An Upper bound for a Communication Game Related to Time-space Tradeoffs -- How Abelian is a Finite Group? -- One Small Size Approximation Models -- The Erdös Existence Argument -- Part IV Geometry -- Introduction -- Extension of Functional Equations -- Remarks on Penrose Tilings -- Distances in Convex Polygons -- Unexpected Applications of Polynomials in Combinatorics -- The Number of Homothetic Subsets -- On Lipschitz Mappings Onto a Square -- A Remark on Transversal Numbers -- In Praise of the Gram Matrix -- On Mutually Avoiding Sets -- Bibliography.
Vol. 2. : Part I Combinatorics and Graph Theory -- Introduction -- Reconstruction Problems for Digraphs -- Neighborly Families of Boxes and Bipartite Coverings -- On the Isolation of a Common Secret -- Properties of Graded Posets Preserved by Some Operations -- The Dimension of Random Graph Orders -- Hereditary and Monotone Properties of Graphs -- Cycles and Paths in Triangle-Free Graphs -- Problems in Graph Theory from Memphis -- Some Remarks on the Cycle Plus Triangles Problem -- Intersection Representations of the Complete Bipartite Graph -- Reflections on a Problem of Erdös and Hajnal -- The Chromatic Number of the Two-Packing of a Forest -- Part II Ramsey and Extremal Theory -- Introduction -- Ramsey Theory in the Work of Paul Erdös -- Memories on Shadows and Shadows of Memories -- A Bound of the Cardinality of Families Not Containing D-Systems -- Flag Algebras: An Interim Report -- Arrangeability and Clique Subdivisions -- A Finite Partition Theorem with Double Exponential Bound -- Paul Erdös' Influence on Extremal Graph Theory -- Applications of the Probabilistic Method to Partially Ordered Sets -- Part III Infinity -- Introduction -- A Few Remarks on a Conjecture of Erdös on the Infinite Version of Menger's Theorem -- The Random Graph -- Paul Erdös' Set Theory -- Set Theory: Geometric and Real -- On Order-Perfect Lattices -- The PCF Theorem Revisited -- Paul Erdös: The Master of Collaboration -- List of Publications of Paul Erdoos --
Summary: Here is a comprehensive overview of the mathematical life of Paul Erdos (1913-1996), a versatile and prolific mathematician. This second volume covers graph theory and combinatorics, extremal and Ramsey theory, and Erdos's research on set theory.
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"List of publications of Paul Erdos, January 2013": v. 2, p. [497]-603.

Includes bibliographical references.

Vol. 1. : Paul Erdos: Life and Work --
Paul Erdoos Magic --
Part I Early Days --
Introduction --
Some of My Favorite Problems and Results --
3 Encounters with Paul Erdös --
4 Did Erdös Save Western Civilization? --
Integers Uniquely Represented by Certain Ternary Forms --
Did Erdös Save Western Civilization? --
Encounters with Paul Erdös --
On Cubic Graphs of Girth at Least Five --
Part II Number Theory --
Introduction --
Cross-disjoint Pairs of Clouds in the Interval Lattice --
Classical Results on Primitive and Recent Results on Cross-Primitive Sequences --
Dense Difference Sets and their Combinatorial Structure --
Integer Sets Containing No Solution to x+y=3z --
On Primes Recognizable in Deterministic Polynomial Time --
Ballot Numbers, Alternating Products, and the Erdös-Heilbronn Conjecture --
On Landau's Function g(n) --
On Divisibility Properties on Sequences of Integers --
On Additive Representation Functions --
Arithmetical Properties of Polynomials --
Some Methods of Erdös Applied to Finite Arithmetic Progressions --
Sur La Non-Dérivabilité de Fonctions Périodiques Associées à Certaines Formules Sommatoires --
1105: First Steps in a Mysterious Quest --
Part III Randomness and Applications --
Introduction --
Games, Randomness, and Algorithms --
The Origins of the Theory of Random Graphs --
An Upper bound for a Communication Game Related to Time-space Tradeoffs --
How Abelian is a Finite Group? --
One Small Size Approximation Models --
The Erdös Existence Argument --
Part IV Geometry --
Introduction --
Extension of Functional Equations --
Remarks on Penrose Tilings --
Distances in Convex Polygons --
Unexpected Applications of Polynomials in Combinatorics --
The Number of Homothetic Subsets --
On Lipschitz Mappings Onto a Square --
A Remark on Transversal Numbers --
In Praise of the Gram Matrix --
On Mutually Avoiding Sets --
Bibliography.

Vol. 2. : Part I Combinatorics and Graph Theory --
Introduction --
Reconstruction Problems for Digraphs --
Neighborly Families of Boxes and Bipartite Coverings --
On the Isolation of a Common Secret --
Properties of Graded Posets Preserved by Some Operations --
The Dimension of Random Graph Orders --
Hereditary and Monotone Properties of Graphs --
Cycles and Paths in Triangle-Free Graphs --
Problems in Graph Theory from Memphis --
Some Remarks on the Cycle Plus Triangles Problem --
Intersection Representations of the Complete Bipartite Graph --
Reflections on a Problem of Erdös and Hajnal --
The Chromatic Number of the Two-Packing of a Forest --
Part II Ramsey and Extremal Theory --
Introduction --
Ramsey Theory in the Work of Paul Erdös --
Memories on Shadows and Shadows of Memories --
A Bound of the Cardinality of Families Not Containing D-Systems --
Flag Algebras: An Interim Report --
Arrangeability and Clique Subdivisions --
A Finite Partition Theorem with Double Exponential Bound --
Paul Erdös' Influence on Extremal Graph Theory --
Applications of the Probabilistic Method to Partially Ordered Sets --
Part III Infinity --
Introduction --
A Few Remarks on a Conjecture of Erdös on the Infinite Version of Menger's Theorem --
The Random Graph --
Paul Erdös' Set Theory --
Set Theory: Geometric and Real --
On Order-Perfect Lattices --
The PCF Theorem Revisited --
Paul Erdös: The Master of Collaboration --
List of Publications of Paul Erdoos --

Here is a comprehensive overview of the mathematical life of Paul Erdos (1913-1996), a versatile and prolific mathematician. This second volume covers graph theory and combinatorics, extremal and Ramsey theory, and Erdos's research on set theory.

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