Combinatorics and Complexity of Partition Functions (Algorithms and Combinatorics)

Alexander Barvinok

  • 出版商: Springer
  • 出版日期: 2017-03-21
  • 售價: $5,020
  • 貴賓價: 9.5$4,769
  • 語言: 英文
  • 頁數: 303
  • 裝訂: Hardcover
  • ISBN: 3319518283
  • ISBN-13: 9783319518282
  • 相關分類: Algorithms-data-structures
  • 海外代購書籍(需單獨結帳)

商品描述

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. 

商品描述(中文翻譯)

分割函數在組合學和統計物理的相關問題中出現,因為它們以簡潔的方式編碼了複雜系統的組合結構。本書的主要焦點是高效計算(近似)各種分割函數,例如永久、哈夫尼恩和它們的高維版本、圖和超圖匹配多項式、圖的獨立多項式以及列舉多面體中的0-1和整數點的分割函數,這使得在原本棘手的問題中可以進行算法上的進展。

本書將散落在文獻中的各種結果統一起來,主要集中在三個主要方法上:縮放、插值和相關衰減。先備知識包括適量的實分析、復分析和線性代數,使得本書對高級數學和物理本科生易於理解。