Combinatorics and Complexity of Partition Functions

Nonfiction, Science & Nature, Mathematics, Combinatorics, Applied
Cover of the book Combinatorics and Complexity of Partition Functions by Alexander Barvinok, Springer International Publishing
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Author: Alexander Barvinok ISBN: 9783319518299
Publisher: Springer International Publishing Publication: March 13, 2017
Imprint: Springer Language: English
Author: Alexander Barvinok
ISBN: 9783319518299
Publisher: Springer International Publishing
Publication: March 13, 2017
Imprint: Springer
Language: English

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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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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