Combinatorics and Complexity of Partition Functions
Springer International Publishing (Verlag)
978-3-319-51828-2 (ISBN)
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.
Alexander Barvinok is a professor of mathematics at the University of Michigan in Ann Arbor, interested in computational complexity and algorithms in algebra, geometry and combinatorics. The reader might be familiar with his books “A Course in Convexity” (AMS, 2002) and “Integer Points in Polyhedra” (EMS, 2008)
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.
"The book is aimed at graduate students and researchers in theoretical computer science, combinatorics and statistical physics. ... The author has the ability to make complicated proofs very accessible while not sacrificing any mathematical rigour, making it a pleasure to read. ... The book also moves from the particular to the general ... . An advantage of this is that it makes it easier to understand the key ideas." (Guus Regts, Mathematical Reviews, August, 2018)
“The book is aimed at graduate students and researchers in theoretical computer science, combinatorics and statistical physics. … The author has the ability to make complicated proofs very accessible while not sacrificing any mathematical rigour, making it a pleasure to read. … The book also moves from the particular to the general … . An advantage of this is that it makes it easier to understand the key ideas.” (Guus Regts, Mathematical Reviews, August, 2018)
| Erscheinungsdatum | 07.03.2017 |
|---|---|
| Reihe/Serie | Algorithms and Combinatorics |
| Zusatzinfo | VI, 303 p. 51 illus., 42 illus. in color. |
| Verlagsort | Cham |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Angewandte Mathematik |
| Schlagworte | Algorithmic Complexity • algorithms • Approximations and Expansions • combinatorics • Combinatorics and graph theory • Complexity • Complex Systems • correlation decay • Differential calculus and equations • Discrete Mathematics • Discrete mathematics in computer science • Dynamics and statics • graph homomorphism • independence polynomial • integer flow • Interpolation • Mathematical Modelling • Mathematics • mathematics and statistics • Mathematics of Algorithmic Complexity • mathing polynomial • Maths for computer scientists • Numerical analysis • partition function • Permanent • scaling • stable polynomials • Statistical Physics |
| ISBN-10 | 3-319-51828-3 / 3319518283 |
| ISBN-13 | 978-3-319-51828-2 / 9783319518282 |
| Zustand | Neuware |
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