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Record Nr. |
UNINA9910254078803321 |
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Autore |
Barvinok Alexander |
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Titolo |
Combinatorics and Complexity of Partition Functions / / by Alexander Barvinok |
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Pubbl/distr/stampa |
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Cham : , : Springer International Publishing : , : Imprint : Springer, , 2016 |
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ISBN |
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Edizione |
[1st ed. 2016.] |
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Descrizione fisica |
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1 online resource (304 pages) : illustrations |
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Collana |
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Algorithms and Combinatorics, , 0937-5511 ; ; 30 |
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Disciplina |
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Soggetti |
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Algorithms |
Combinatorics |
Computer science—Mathematics |
Statistical physics |
Dynamical systems |
Approximation theory |
Mathematics of Algorithmic Complexity |
Discrete Mathematics in Computer Science |
Complex Systems |
Approximations and Expansions |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Nota di bibliografia |
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Includes bibliographical references and index. |
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Nota di contenuto |
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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. |
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Sommario/riassunto |
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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 |
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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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