Combinatorics and Complexity of Partition Functions

Alexander Barvinok

ISBN 10: 3319518283 / ISBN 13: 9783319518282

Published by Springer International Publishing, Springer International Publishing Mär 2017, 2017

About this Item

This item is printed on demand - Print on Demand Titel. Neuware -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.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 312 pp. Englisch.

Seller Inventory # 9783319518282

Bibliographic Details

• Title: Combinatorics and Complexity of Partition Functions
• Publisher: Springer International Publishing, Springer International Publishing Mär 2017
• Publication Date: 2017
• Language: English
• ISBN 10: 3319518283
• ISBN 13: 9783319518282
• Binding: Buch
• Condition: Neu

About this title

Synopsis

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. 

About the Author

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)