Combinatorics and Complexity of Partition Functions (Algorithms and Combinatorics (30))

Barvinok, Alexander

ISBN 10: 3319847511 / ISBN 13: 9783319847511

Published by Springer, 2018

About this Item

PRINT ON DEMAND pp. 309.

Seller Inventory # 18384201127

Bibliographic Details

• Title: Combinatorics and Complexity of Partition Functions (Algorithms and Combinatorics (30))
• Publisher: Springer
• Publication Date: 2018
• Language: English
• ISBN 10: 3319847511
• ISBN 13: 9783319847511
• Binding: Soft cover
• Condition: New

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)