Overview
- Contains an exposition of recent results
- Demonstrates a unified approach to hard algorithmic problems
- Provides an easy to read introduction to statistical physics phenomena
- Includes supplementary material: sn.pub/extras
Part of the book series: Algorithms and Combinatorics (AC, volume 30)
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About this book
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.
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Keywords
Table of contents (8 chapters)
Reviews
“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)
Authors and Affiliations
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)
Bibliographic Information
Book Title: Combinatorics and Complexity of Partition Functions
Authors: Alexander Barvinok
Series Title: Algorithms and Combinatorics
DOI: https://doi.org/10.1007/978-3-319-51829-9
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing AG 2016
Hardcover ISBN: 978-3-319-51828-2Published: 21 March 2017
Softcover ISBN: 978-3-319-84751-1Published: 18 July 2018
eBook ISBN: 978-3-319-51829-9Published: 13 March 2017
Series ISSN: 0937-5511
Series E-ISSN: 2197-6783
Edition Number: 1
Number of Pages: VI, 303
Number of Illustrations: 9 b/w illustrations, 42 illustrations in colour
Topics: Mathematics of Algorithmic Complexity, Combinatorics, Discrete Mathematics in Computer Science, Complex Systems, Algorithms, Approximations and Expansions