This volume is dedicated to Paul Erdos, who profoundly influenced mathematics in the twentieth century, with over 1200 papers in number theory, complex analysis, probability theory, geometry, interpretation theory, algebra set theory and combinatorics. One of Erdos' hallmarks was the host of stimulating problems and conjectures, to many of which he attached monetary prices, in accordance with their notoriety. A feature of this volume is a collection of some 50 outstanding unsolved problems, together with their 'value'! Eminent mathematicians from around the world have contributed articles to this volume that reflect the diversity of Erdos' interests, and it will be a fund of insight for number theorists, combinatorialists, set theorists and analysts.

Combinatorics is an active field of mathematical study and the British Combinatorial Conference, held biennially, aims to survey the most important developments by inviting distinguished mathematicians to lecture at the meeting. The contributions of the principal lecturers at the Seventh Conference, held in Cambridge, are published here and the topics reflect the breadth of the subject. Each author has written a broadly conceived survey, not limited to his own work, but intended for wide readership. Important aspects of the subject are emphasized so that non-specialists will find them understandable. Topics covered include graph theory, matroids, combinatorial set theory, projective geometry and combinatorial group theory. All those researching into any aspect of Combinatorics and its applications will find much in these articles of use and interest.

This volume is dedicated to Paul Erdos, who profoundly influenced mathematics in the twentieth century, with over 1200 papers in number theory, complex analysis, probability theory, geometry, interpretation theory, algebra set theory and combinatorics. One of Erdos' hallmarks was the host of stimulating problems and conjectures, to many of which he attached monetary prices, in accordance with their notoriety. A feature of this volume is a collection of some 50 outstanding unsolved problems, together with their 'value'! Eminent mathematicians from around the world have contributed articles to this volume that reflect the diversity of Erdos' interests, and it will be a fund of insight for number theorists, combinatorialists, set theorists and analysts.

Combinatorics is an active field of mathematical study and the British Combinatorial Conference, held biennially, aims to survey the most important developments by inviting distinguished mathematicians to lecture at the meeting. The contributions of the principal lecturers at the Seventh Conference, held in Cambridge, are published here and the topics reflect the breadth of the subject. Each author has written a broadly conceived survey, not limited to his own work, but intended for wide readership. Important aspects of the subject are emphasized so that non-specialists will find them understandable. Topics covered include graph theory, matroids, combinatorial set theory, projective geometry and combinatorial group theory. All those researching into any aspect of Combinatorics and its applications will find much in these articles of use and interest.