04069nam 22007335 450 991025407880332120250609111446.03-319-51829-110.1007/978-3-319-51829-9(CKB)3710000001100884(MiAaPQ)EBC4822606(DE-He213)978-3-319-51829-9(PPN)199767467(MiAaPQ)EBC6237365(EXLCZ)99371000000110088420170314d2016 u| 0engurcnu||||||||rdacontentrdamediardacarrierCombinatorics and Complexity of Partition Functions /by Alexander Barvinok1st ed. 2016.Cham :Springer International Publishing :Imprint: Springer,2016.1 online resource (304 pages) illustrationsAlgorithms and Combinatorics,0937-5511 ;303-319-51828-3 Includes bibliographical references and index.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. .Algorithms and Combinatorics,0937-5511 ;30AlgorithmsCombinatorial analysisComputer science—MathematicsStatistical physicsDynamicsApproximation theoryMathematics of Algorithmic Complexityhttps://scigraph.springernature.com/ontologies/product-market-codes/M13130Combinatoricshttps://scigraph.springernature.com/ontologies/product-market-codes/M29010Discrete Mathematics in Computer Sciencehttps://scigraph.springernature.com/ontologies/product-market-codes/I17028Complex Systemshttps://scigraph.springernature.com/ontologies/product-market-codes/P33000Algorithmshttps://scigraph.springernature.com/ontologies/product-market-codes/M14018Approximations and Expansionshttps://scigraph.springernature.com/ontologies/product-market-codes/M12023Algorithms.Combinatorial analysis.Computer science—Mathematics.Statistical physics.Dynamics.Approximation theory.Mathematics of Algorithmic Complexity.Combinatorics.Discrete Mathematics in Computer Science.Complex Systems.Algorithms.Approximations and Expansions.510Barvinok Alexanderauthttp://id.loc.gov/vocabulary/relators/aut322075MiAaPQMiAaPQMiAaPQBOOK9910254078803321Combinatorics and complexity of partition functions1523225UNINA