Combinatorics and Complexity of Partition Functions
Authors: Barvinok, Alexander
Free Preview- Contains an exposition of recent results
- Demonstrates a unified approach to hard algorithmic problems
- Provides an easy to read introduction to statistical physics phenomena
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- About this book
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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 authors
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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)
- Reviews
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“The book is aimed at graduate students and researchers in theoretical computer science, combinatorics and statistical physics. … The author has the ability to make complicated proofs very accessible while not sacrificing any mathematical rigour, making it a pleasure to read. … The book also moves from the particular to the general … . An advantage of this is that it makes it easier to understand the key ideas.” (Guus Regts, Mathematical Reviews, August, 2018)
- Table of contents (8 chapters)
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Introduction
Pages 1-7
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Preliminaries
Pages 9-45
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Permanents
Pages 47-92
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Hafnians and Multidimensional Permanents
Pages 93-143
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The Matching Polynomial
Pages 145-179
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Table of contents (8 chapters)
- Download Sample pages 1 PDF (148.9 KB)
- Download Sample pages 3 PDF (719.7 KB)
- Download Table of contents PDF (96.6 KB)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- Combinatorics and Complexity of Partition Functions
- Authors
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- Alexander Barvinok
- Series Title
- Algorithms and Combinatorics
- Series Volume
- 30
- Copyright
- 2016
- Publisher
- Springer International Publishing
- Copyright Holder
- Springer International Publishing AG
- eBook ISBN
- 978-3-319-51829-9
- DOI
- 10.1007/978-3-319-51829-9
- Hardcover ISBN
- 978-3-319-51828-2
- Softcover ISBN
- 978-3-319-84751-1
- Series ISSN
- 0937-5511
- Edition Number
- 1
- Number of Pages
- VI, 303
- Number of Illustrations
- 9 b/w illustrations, 42 illustrations in colour
- Topics
