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Combinatorics and Complexity of Partition Functions (Algorithms and Combinatorics, 30) - Hardcover

 
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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. 

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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)

Review

“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)

"About this title" may belong to another edition of this title.

  • PublisherSpringer
  • Publication date2017
  • ISBN 10 3319518283
  • ISBN 13 9783319518282
  • BindingHardcover
  • LanguageEnglish
  • Edition number1
  • Number of pages309

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ISBN 10:  3319847511 ISBN 13:  9783319847511
Publisher: Springer, 2018
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Buch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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. 312 pp. Englisch. Seller Inventory # 9783319518282

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Buch. Condition: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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. Seller Inventory # 9783319518282

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Condition: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Contains an exposition of recent results&nbspDemonstrates a unified approach to hard algorithmic problemsProvides an easy to read introduction to statistical physics phenomena Contains an ex. Seller Inventory # 135466928

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