TY - BOOK ID - 21740638 TI - Combinatorics and Complexity of Partition Functions PY - 2016 SN - 3319518291 3319518283 PB - Cham : Springer International Publishing : Imprint: Springer, DB - UniCat KW - Combinatorial analysis. KW - Partitions (Mathematics) KW - Combinatorics KW - Number theory KW - Algebra KW - Mathematical analysis KW - Combinatorics. KW - Computational complexity. KW - Algorithms. KW - Mathematics. KW - Mathematics of Algorithmic Complexity. KW - Discrete Mathematics in Computer Science. KW - Complex Systems. KW - Approximations and Expansions. KW - Math KW - Science KW - Algorism KW - Arithmetic KW - Complexity, Computational KW - Electronic data processing KW - Machine theory KW - Foundations KW - Computer science—Mathematics. KW - Statistical physics. KW - Dynamical systems. KW - Approximation theory. KW - Theory of approximation KW - Functional analysis KW - Functions KW - Polynomials KW - Chebyshev systems KW - Dynamical systems KW - Kinetics KW - Mathematics KW - Mechanics, Analytic KW - Force and energy KW - Mechanics KW - Physics KW - Statics KW - Mathematical statistics KW - Statistical methods UR - https://www.unicat.be/uniCat?func=search&query=sysid:21740638 AB - 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. . ER -