Combinatorics and complexity of partition functions

• 作者： Barvinok, Alexander, author.
• 其他作者：
  • SpringerLink (Online service)
• 其他題名：
  • Algorithms and combinatorics ;
• 出版： Cham : Springer International Publishing :Imprint: Springer
• 叢書名： Algorithms and combinatorics,volume 30
• 主題： Combinatorial analysis. , Partitions (Mathematics) , Mathematics. , Mathematics of Algorithmic Complexity. , Combinatorics. , Discrete Mathematics in Computer Science. , Complex Systems. , Algorithms. , Approximations and Expansions.
• ISBN： 9783319518299 (electronic bk.) 、 9783319518282 (paper)
• FIND@SFXID: CGU
• 資料類型: 電子書
• 內容註: 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.
• More
• 摘要註: 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.
• 讀者標籤：

  需登入
• 引用連結：

  Copy Link
• 目前引用數
• Share: