Combinatorics is an area of mathematics involving an impressive breadth of ideas, and it encompasses topics ranging from codes and circuit design to algorithmic complexity and algebraic graph theory. In a highly distinguished career Bela Bollobas has made, and continues to make, many significant contributions to combinatorics, and this volume reflects the wide range of topics on which his work has had a major influence. It arises from a conference organized to mark his 60th birthday and the thirty-one articles contained here are of the highest calibre. That so many excellent mathematicians have contributed is testament to the very high regard in which Bela Bollobas is held. Students and researchers across combinatorics and related fields will find that this volume provides a wealth of insight to the state of the art.

Paul Erdoes was one of the greatest mathematicians of this century, known the world over for his brilliant ideas and stimulating questions. On the date of his 80th birthday a conference was held in his honour at Trinity College, Cambridge. Many leading combinatorialists attended. Their subsequent contributions are collected here. The areas represented range from set theory and geometry, through graph theory, group theory and combinatorial probability, to randomised algorithms and statistical physics. Erdoes himself was able to give a survey of recent progress made on his favourite problems. Consequently this volume, consisting of in-depth studies at the frontier of research, provides a valuable panorama across the breadth of combinatorics as it is today.

Paul Erdoes was one of the greatest mathematicians of this century, known the world over for his brilliant ideas and stimulating questions. On the date of his 80th birthday a conference was held in his honour at Trinity College, Cambridge. Many leading combinatorialists attended. Their subsequent contributions are collected here. The areas represented range from set theory and geometry, through graph theory, group theory and combinatorial probability, to randomised algorithms and statistical physics. Erdoes himself was able to give a survey of recent progress made on his favourite problems. Consequently this volume, consisting of in-depth studies at the frontier of research, provides a valuable panorama across the breadth of combinatorics as it is today.

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