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Field name	Details
Dewey Class	511.352
Title	Combinatorics and Complexity of Partition Functions ([EBook]) / by Alexander Barvinok.
Author	Barvinok, Alexander
Other name(s)	SpringerLink (Online service)
Publication	Cham : : Springer International Publishing : : Imprint: Springer, , 2016.
Physical Details	VI, 303 p. 51 illus., 42 illus. in color. : online resource.
Series	Algorithms and Combinatorics 0937-5511 ; ; 30
ISBN	9783319518299
Summary Note	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. .:
Contents note	Chapter I. Introduction -- Chapter II. Preliminaries -- Chapter III. Permanents -- Chapter IV. Hafnians and Multidimensional Permanents -- Chapter V. The Matching Polynomial -- Chapter VI. The Independence Polynomial -- Chapter VII. The Graph Homomorphism Partition Function -- Chapter VIII. Partition Functions of Integer Flows -- References -- Index.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-3-319-51829-9
Links to Related Works	Subject References: Algorithms . Approximation theory . Approximations and Expansions . Combinatorics . Complex Systems . Computer Science . Discrete Mathematics in Computer Science . Mathematics . Mathematics of Algorithmic Complexity . System theory . Authors: Barvinok, Alexander . Corporate Authors: SpringerLink (Online service) . Series: Algorithms and Combinatorics . Classification: 511.352 .

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Combinatorics and Complexity of Partition Functions

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