Combinatorics and Complexity of Partition Functions

1. Auflage 2016
ISBN: 978-3-319-51828-2
Verlag: Springer International Publishing

Buch, Englisch, Band 30, 303 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 5915 g

Reihe: Algorithms and Combinatorics

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. 

Zielgruppe

Graduate

Autoren/Hrsg.

Barvinok, Alexander

Fachgebiete

• Mathematik | Informatik EDV | Informatik Programmierung | Softwareentwicklung Algorithmen & Datenstrukturen
• Mathematik | Informatik Mathematik Mathematik Allgemein Diskrete Mathematik, Kombinatorik
• Mathematik | Informatik EDV | Informatik Informatik Mathematik für Informatiker
• Mathematik | Informatik EDV | Informatik Informatik Berechenbarkeitstheorie, Komplexitätstheorie
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
• Naturwissenschaften Physik Angewandte Physik Statistische Physik, Dynamische Systeme

Inhaltsverzeichnis

Chapter I. Introduction.- Chapter II. Preliminaries.- Chapter III. Permanents.- Chapter IV. Hafnians and Multidimensional Permanents.- Chapter V. The Matching Polynomial.- Chapter VI. The Independence Polynomial.- Chapter VII. The Graph Homomorphism Partition Function.- Chapter VIII. Partition Functions of Integer Flows.- References.- Index.

Über Autor(innen)

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)