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The Mathematics of Paul Erdös I

  • Book
  • © 1997

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Editors:
  1. Ronald L. Graham

    1. AT&T Bell Laboratories, Murray Hill, USA

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  2. Jaroslav Nešetřil

    1. Department of Applied Mathematics, Charles University, Praha, Czech Republic

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    You can also search for this editor in PubMed   Google Scholar

Part of the book series: Algorithms and Combinatorics (AC, volume 13)

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Table of contents (29 chapters)

  1. Front Matter

    Pages I-XVI
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  2. Paul Erdős — Life and Work

    1. Paul Erdős — Life and Work

      • Béla Bollobás
      Pages 1-41

  3. Early Days

    1. Front Matter

      Pages 43-43
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    2. Introduction

      • Ronald L. Graham, Jaroslav Nešetřil
      Pages 45-46

    3. Some of My Favorite Problems and Results

      • Paul Erdős
      Pages 47-67

    4. Encounters with Paul Erdős

      • A. H. Stone
      Pages 68-73

    5. Did Erdős Save Western Civilization?

      • Cedric A. B. Smith
      Pages 74-85

    6. Integers Uniquely Represented by Certain Ternary Forms

      • Irving Kaplansky
      Pages 86-94

    7. On Cubic Graphs of Girth at Least Five

      • W. T. Tutte
      Pages 95-97

  4. Number Theory

    1. Front Matter

      Pages 99-99
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    2. Introduction

      • Ronald L. Graham, Jaroslav Nešetřil
      Pages 101-103

    3. Classical Results on Primitive and Recent Results on Cross-Primitive Sequences

      • Rudolf Ahlswede, Levon H. Khachatrian
      Pages 104-116

    4. Sur La Non-Dérivabilité de Fonctions Périodiques Associées à Certaines Formules Sommatoires

      • Gérald Tenenbaum
      Pages 117-128

    5. On Additive Representation Functions

      • A. Sárközy, V. T. Sós
      Pages 129-150

    6. Arithmetical Properties of Polynomials

      • A. Schinzel
      Pages 151-154

    7. Cross-Disjoint Pairs of Clouds in the Interval Lattice

      • Rudolf Ahlswede, Ning Cai
      Pages 155-164

    8. Dense Difference Sets and their Combinatorial Structure

      • Vitaly Bergelson, Paul Erdös, Neil Hindman, Tomasz Łuczak
      Pages 165-175

    9. On Primes Recognizable in Deterministic Polynomial Time

      • Sergei Konyagin, Carl Pomerance
      Pages 176-198

    10. Ballot Numbers, Alternating Products, and the Erdős-Heilbronn Conjecture

      • Melvyn B. Nathanson
      Pages 199-217

    11. Integer Sets Containing no Solution to x + y = 3z

      • Fan R. K. Chung, John L. Goldwasser
      Pages 218-227
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Keywords

About this book

In 1992, when Paul Erdos was awarded a Doctor Honoris Causa by Charles University in Prague, a small conference was held, bringing together a distin­ guished group of researchers with interests spanning a variety of fields related to Erdos' own work. At that gathering, the idea occurred to several of us that it might be quite appropriate at this point in Erdos' career to solicit a col­ lection of articles illustrating various aspects of Erdos' mathematical life and work. The response to our solicitation was immediate and overwhelming, and these volumes are the result. Regarding the organization, we found it convenient to arrange the papers into six chapters, each mirroring Erdos' holistic approach to mathematics. Our goal was not merely a (random) collection of papers but rather a thor­ oughly edited volume composed in large part by articles explicitly solicited to illustrate interesting aspects of Erdos and his life and work. Each chap­ ter includes an introduction which often presents a sample of related ErdOs' problems "in his own words". All these (sometimes lengthy) introductions were written jointly by editors. We wish to thank the nearly 70 contributors for their outstanding efforts (and their patience). In particular, we are grateful to Bela Bollobas for his extensive documentation of Paul Erdos' early years and mathematical high points (in the first part of this volume); our other authors are acknowledged in their respective chapters. We also want to thank A. Bondy, G. Hahn, I.

Editors and Affiliations

  • AT&T Bell Laboratories, Murray Hill, USA

    Ronald L. Graham

  • Department of Applied Mathematics, Charles University, Praha, Czech Republic

    Jaroslav Nešetřil

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