TY  - BOOK
AU  - Barvinok, Alexander
TI  - Combinatorics and complexity of partition functions
SN  - 9783319847511
U1  - 512.73 BAR-A 
PY  - 2017///
CY  - USA
PB  - Springer
KW  - Combinatorial analysis
KW  - Partitions (Mathematics)
KW  - Mathematics
KW  - Algorithms
KW  - System theory
KW  - Approximation theory
KW  - Computer science--Mathematics
KW  - Computational complexity
N1  - 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, hafnia 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  -