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Cuts and metrics are well-known objects that arise - independently, but with many deep and fascinating connections - in diverse fields: in graph theory, combinatorial optimization, geometry of numbers, distance geometry, combinatorial matrix theory, statistical physics, VLSI design etc. A main feature of this book is its interdisciplinarity. The book contains a wealth of results, from different mathematical disciplines, which are presented here in a unified and comprehensive manner. Geometric representations and methods turn out to be the linking theme. This book will provide a unique and invaluable source for researchers and graduate students. From the Reviews: "This book is definitely a milestone in the literature of integer programming and combinatorial optimization. It draws from the interdisciplinarity of these fields as it gathers methods and results from polytope theory, geometry of numbers, probability theory, design and graph theory around two objects, cuts and metrics. [… ] The book is very nicely written [… ] The book is also very well structured. With knowledge about the relevant terms, one can enjoy special subsections without being entirely familiar with the rest of the chapter. This makes it not only an interesting research book but even a dictionary. [… ] In my opinion, the book is a beautiful piece of work. The longer one works with it, the more beautiful it becomes." Robert Weismantel, Optima 56 (1997) "… In short, this is a very interesting book which is nice to have." Alexander I. Barvinok, MR 1460488 (98g:52001) "… This is a large and fascinating book. As befits a book which contains material relevant to so many areas of mathematics (and related disciplines such as statistics, physics, computing science, and economics), it is self-contained and written in a readable style. Moreover, the index, bibliography, and table of contents are all that they should be in such a work; it is easy to find as much or as little introductory material as needed." R.Dawson, Zentralblatt MATH Database 0885.52001.

Discrete mathematics --- Graph theory --- Metric spaces --- Embeddings (Mathematics) --- Théorie des graphes --- Espaces métriques --- Plongements (Mathématiques) --- Graph theory. --- Metric spaces. --- Embeddings (Mathematics). --- Théorie des graphes --- Espaces métriques --- Plongements (Mathématiques) --- Discrete mathematics. --- Geometry. --- Combinatorics. --- Convex geometry . --- Discrete geometry. --- Number theory. --- Discrete Mathematics. --- Graph Theory. --- Convex and Discrete Geometry. --- Number Theory. --- Number study --- Numbers, Theory of --- Algebra --- Geometry --- Combinatorial geometry --- Combinatorics --- Mathematical analysis --- Graphs, Theory of --- Theory of graphs --- Combinatorial analysis --- Topology --- Mathematics --- Euclid's Elements --- Discrete mathematical structures --- Mathematical structures, Discrete --- Structures, Discrete mathematical --- Numerical analysis --- Extremal problems