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Algorithms and Combinatorics

Combinatorics and Complexity of Partition Functions

Authors: Barvinok, Alexander

  • 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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eBook 91,62 €
price for Spain (gross)
  • ISBN 978-3-319-51829-9
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 114,39 €
price for Spain (gross)
  • ISBN 978-3-319-51828-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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. 

About the authors

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)

Table of contents (8 chapters)

Buy this book

eBook 91,62 €
price for Spain (gross)
  • ISBN 978-3-319-51829-9
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 114,39 €
price for Spain (gross)
  • ISBN 978-3-319-51828-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Combinatorics and Complexity of Partition Functions
Authors
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
Series ISSN
0937-5511
Edition Number
1
Number of Pages
VI, 303
Number of Illustrations and Tables
9 b/w illustrations, 42 illustrations in colour
Topics