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＜電子ブック＞
Combinatorics and Complexity of Partition Functions / by Alexander Barvinok
(Algorithms and Combinatorics. ISSN:21976783 ; 30)

版	1st ed. 2016.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2016
大きさ	VI, 303 p. 51 illus., 42 illus. in color : online resource
著者標目	*Barvinok, Alexander author SpringerLink (Online service)
件　名	LCSH:Mathematics LCSH:Discrete mathematics LCSH:Computer science—Mathematics LCSH:System theory LCSH:Algorithms LCSH:Approximation theory FREE:Applications of Mathematics FREE:Discrete Mathematics FREE:Discrete Mathematics in Computer Science FREE:Complex Systems FREE:Algorithms FREE:Approximations and Expansions
一般注記	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 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. HTTP:URL=https://doi.org/10.1007/978-3-319-51829-9

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