Combinatorics and Complexity of Partition Functions

Alexander Barvinok

ISBN 10: 3319518283 / ISBN 13: 9783319518282

Verlag: Springer International Publishing, Springer International Publishing, 2017

Beschreibung

Druck auf Anfrage Neuware - Printed after ordering - Partition functions arise in combinatorics and related problems of statistical physics as they encode in a succinct way the combinatorial structure of complicated systems. The main focus of the book is on efficient ways to compute (approximate) various partition functions, such as permanents, hafnians and their higher-dimensional versions, graph and hypergraph matching polynomials, the independence polynomial of a graph and partition functions enumerating 0-1 and integer points in polyhedra, which allows one to make algorithmic advances in otherwise intractable problems.The book unifies various, often quite recent, results scattered in the literature, concentrating on the three main approaches: scaling, interpolation and correlation decay.The prerequisites include moderate amounts of real and complex analysis and linear algebra, making the book accessible to advanced math and physics undergraduates.

Bestandsnummer des Verkäufers 9783319518282

Bibliografische Details

• Titel: Combinatorics and Complexity of Partition Functions
• Verlag: Springer International Publishing, Springer International Publishing
• Erscheinungsjahr: 2017
• Sprache: Englisch
• ISBN-10: 3319518283
• ISBN-13: 9783319518282
• Einband: Buch
• Zustand: Neu

Über diesen Titel

Inhaltsangabe

Partition functions arise in combinatorics and related problems of statistical physics as they encode in a succinct way the combinatorial  structure of complicated systems. The main focus of the book is on efficient ways to compute (approximate) various partition functions, such as permanents, hafnians and their higher-dimensional versions, graph and hypergraph matching polynomials, the independence polynomial of a graph and partition functions enumerating 0-1 and integer points in polyhedra, which allows one to make algorithmic advances in otherwise intractable problems. 

The book unifies various, often quite recent, results scattered in the literature, concentrating on the three main approaches: scaling, interpolation and correlation decay. The prerequisites include moderate amounts of real and complex analysis and linear algebra, making the book accessible to advanced math and physics undergraduates. 

Über die Autorin bzw. den Autor

Alexander Barvinok is a professor of mathematics at the University of Michigan in Ann Arbor, interested in computational complexity and algorithms in algebra, geometry and combinatorics. The reader might be familiar with his books “A Course in Convexity” (AMS, 2002) and “Integer Points in Polyhedra” (EMS, 2008)