# Combinatorics and Complexity of Partition Functions

- 17 Citations
- 3 Mentions
- 10k Downloads

Part of the Algorithms and Combinatorics book series (AC, volume 30)

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- 17 Citations
- 3 Mentions
- 10k Downloads

Part of the Algorithms and Combinatorics book series (AC, volume 30)

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 complexity partition function permanent mathing polynomial independence polynomial graph homomorphism integer flow stable polynomials correlation decay interpolation scaling

- DOI https://doi.org/10.1007/978-3-319-51829-9
- Copyright Information Springer International Publishing AG 2016
- Publisher Name Springer, Cham
- eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
- Print ISBN 978-3-319-51828-2
- Online ISBN 978-3-319-51829-9
- Series Print ISSN 0937-5511
- Series Online ISSN 2197-6783
- Buy this book on publisher's site