The mathematics of Paul Erdös
著者
書誌事項
The mathematics of Paul Erdös
Springer, c2013
2nd ed
- 1
- 2
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注記
Includes bibliographical references
List of publications of Paul Erdős, January 2013: v.2: p. 497-603
内容説明・目次
- 巻冊次
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2 ISBN 9781461472537
内容説明
This is the most comprehensive survey of the mathematical life of the legendary Paul Erdos (1913-1996), one of the most versatile and prolific mathematicians of our time. For the first time, all the main areas of Erdos' research are covered in a single project. Because of overwhelming response from the mathematical community, the project now occupies over 1000 pages, arranged into two volumes. These volumes contain both high level research articles as well as key articles that survey some of the cornerstones of Erdos' work, each written by a leading world specialist in the field. A special chapter "Early Days", rare photographs, and art related to Erdos complement this striking collection. A unique contribution is the bibliography on Erdos' publications: the most comprehensive ever published. This new edition, dedicated to the 100th anniversary of Paul Erdos' birth, contains updates on many of the articles from the two volumes of the first edition, several new articles from prominent mathematicians, a new introduction, and more biographical information about Paul Erdos with an updated list of publications.
The second volume contains chapters on graph theory and combinatorics, extremal and Ramsey theory, and a section on infinity that covers Erdos' research on set theory. All of these chapters are essentially updated, particularly the extremal theory chapter that contains a survey of flag algebras, a new technique for solving extremal problems.
目次
VOLUME II.- 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 Erdos 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 Erdos.- Memories on Shadows and Shadows of Memories.- A Bound of the Cardinality of Families Not Containing -Systems.- Flag Algebras: An Interim Report.- Arrangeability and Clique Subdivisions.- A Finite Partition Theorem with Double Exponential Bound.- Paul Erdos' 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 Erdos on the Infinite Version of Menger's Theorem.- The Random Graph.- Paul Erdos' Set Theory.- Set Theory: Geometric and Real.- On Order-Perfect Lattices.- The PCF Theorem Revisited.- Paul Erdos: The Master of Collaboration.- List of Publications of Paul Erdos.- Postscript.
- 巻冊次
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1 ISBN 9781461472575
内容説明
This is the most comprehensive survey of the mathematical life of the legendary Paul Erdos (1913-1996), one of the most versatile and prolific mathematicians of our time. For the first time, all the main areas of Erdos' research are covered in a single project. Because of overwhelming response from the mathematical community, the project now occupies over 1000 pages, arranged into two volumes. These volumes contain both high level research articles as well as key articles that survey some of the cornerstones of Erdos' work, each written by a leading world specialist in the field. A special chapter "Early Days", rare photographs, and art related to Erdos complement this striking collection. A unique contribution is the bibliography on Erdos' publications: the most comprehensive ever published. This new edition, dedicated to the 100th anniversary of Paul Erdos' birth, contains updates on many of the articles from the two volumes of the first edition, several new articles from prominent mathematicians, a new introduction, more biographical information about Paul Erdos, and an updated list of publications.
The first volume contains the unique chapter "Early Days", which features personal memories of Paul Erdos by a number of his colleagues. The other three chapters cover number theory, random methods, and geometry. All of these chapters are essentially updated, most notably the geometry chapter that covers the recent solution of the problem on the number of distinct distances in finite planar sets, which was the most popular of Erdos' favorite geometry problems.
目次
VOLUME I.- Paul Erdos - Life and Work.- Paul Erdos Magic.- Part I Early Days.- Introduction.- Some of My Favorite Problems and Results.- 3 Encounters with Paul Erdos.- 4 Did Erdos Save Western Civilization?.- Integers Uniquely Represented by Certain Ternary Forms.- Did Erdos Save Western Civilization?.- Encounters with Paul Erdos.- 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 Erdos-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 Erdos Applied to Finite Arithmetic Progressions.- Sur La Non-Derivabilite de Fonctions Periodiques Associees a 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 Erdos 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.
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