A panorama of combinatorics by the world's experts.

This undergraduate textbook is suitable for introductory classes in combinatorics and related topics. The book covers a wide range of both pure and applied combinatorics, beginning with the very basics of enumeration and then going on to Latin squares, graphs and designs. The latter topic is closely related to finite geometry, which is developed in parallel. Applications to probability theory, algebra, coding theory, cryptology and combinatorial game theory comprise the later chapters. Throughout the book, examples and exercises illustrate the material, and the interrelations between the various topics is emphasized. Readers looking to take first steps toward the study of combinatorics, finite geometry, design theory, coding theory, or cryptology will find this book valuable. Essentially self-contained, there are very few prerequisites aside from some mathematical maturity, and the little algebra required is covered in the text. The book is also a valuable resource for anyone interested in discrete mathematics as it ties together a wide variety of topics.

The purpose of this book is to present the three basic ideas of geometrical probability, also known as integral geometry, in their natural framework. In this way, the relationship between the subject and enumerative combinatorics is more transparent, and the analogies can be more productively understood. The first of the three ideas is invariant measures on polyconvex sets. The authors then prove the fundamental lemma of integral geometry, namely the kinematic formula. Finally the analogues between invariant measures and finite partially ordered sets are investigated, yielding insights into Hecke algebras, Schubert varieties and the quantum world, as viewed by mathematicians. Geometers and combinatorialists will find this a most stimulating and fruitful story.

The aim of this book is to provide a thorough introduction to various aspects of trees in random settings and a systematic treatment of the mathematical analysis techniques involved. It should serve as a reference book as well as a basis for future research.

Among the intuitively appealing aspects of graph theory is its close connection to drawings and geometry. The development of computer technology has become a source of motivation to reconsider these connections, in particular geometric graphs are emerging as a new subfield of graph theory. Arrangements of points and lines are the objects for many challenging problems and surprising solutions in combinatorial geometry. The book is a collection of beautiful and partly very recent results from the intersection of geometry, graph theory and combinatorics.

This volume celebrating the 60th birthday of Béla Bollobás presents the state of the art in combinatorics.

This 2005 book deals with interest topics in Discrete and Algorithmic aspects of Geometry.