Combinatorics and Complexity of Partition Functions

• Main Author: Barvinok, Alexander (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2016.
• Series: Algorithms and Combinatorics, 30
• Subjects: Mathematics.; Computer science > Mathematics.; Approximation theory.; System theory.; Algorithms.; Combinatorics.; Mathematics of Algorithmic Complexity.; Discrete Mathematics in Computer Science.; Complex Systems.; Approximations and Expansions.

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...

Table of Contents:

• 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.