The Mathematics of Paul Erdös I

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.

Contenu

of The Mathematics of Paul Erd?s I.- Paul Erd?s - Life and Work.- I. Early Days.- Some of My Favorite Problems and Results.- Encounters with Paul Erd?s.- Did Erd?s Save Western Civilization?.- Integers Uniquely Represented by Certain Ternary Forms.- On Cubic Graphs of Girth at Least Five.- II. Number Theory.- Classical Results on Primitive and Recent Results on Cross-Primitive Sequences.- Sur la Non-dérivabilité de Fonctions Périodiques Associées à Certaines Formules Sommatoires.- On Additive Representation Functions.- Arithmetical Properties of Polynomials.- Cross-Disjoint Pairs of Clouds in the Interval Lattice.- Dense Difference Sets and their Combinatorial Structure.- On Primes Recognizable in Deterministic Polynomial Time.- Ballot Nummbers, Alternating Products, and the Erd?s-Heilbronn Conjecture.- Integer Sets Containing no Solution to x + y = 3z.- On Landau's Function g(n).- On Divisibility Properties of Sequences of Integers.- Some Methods of Erd?s Applied to Finite Arithmetic Progressions.- 1105: First Steps in a Mysterious Quest.- III. Randomness and Applications.- Games, Randomness and Algorithms.- The Origins of the Theory of Random Graphs.- The Erd?s Existence Argument.- On Some Hypergraph Problems of Paul Erd?s and the Asymptotics of Matchings, Covers and Colorings.- How Abelian is a Finite Group?.- On Small Size Approximation Models.- An Upper Bound for a Communication Game Related to Time-Space Tradeoffs.