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Combinatorics and Complexity of Partition Functions (Hardcover, 1st ed. 2016)
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Combinatorics and Complexity of Partition Functions (Hardcover, 1st ed. 2016)
Series: Algorithms and Combinatorics, 30
Expected to ship within 12 - 19 working days
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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 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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