Handbook of the Tutte Polynomial and Related Topics
暫譯: 圖特多項式及相關主題手冊
Ellis-Monaghan, Joanna A., Moffatt, Iain
- 出版商: CRC
- 出版日期: 2022-07-06
- 售價: $8,720
- 貴賓價: 9.5 折 $8,284
- 語言: 英文
- 頁數: 784
- 裝訂: Hardcover - also called cloth, retail trade, or trade
- ISBN: 1482240629
- ISBN-13: 9781482240627
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相關主題
商品描述
The Tutte Polynomial touches on nearly every area of combinatorics as well as many other fields, including statistical mechanics, coding theory, and DNA sequencing. It is one of the most studied graph polynomials.
Handbook of the Tutte Polynomial and Related Topics is the first handbook published on the Tutte Polynomial. It consists of thirty-four chapters written by experts in the field, which collectively offer a concise overview of the polynomial's many properties and applications. Each chapter covers a different aspect of the Tutte polynomial and contains the central results and references for its topic. The chapters are organized into six parts. Part I describes the fundamental properties of the Tutte polynomial, providing an overview of the Tutte polynomial and the necessary background for the rest of the handbook. Part II is concerned with questions of computation, complexity, and approximation for the Tutte polynomial; Part III covers a selection of related graph polynomials; Part IV discusses a range of applications of the Tutte polynomial to mathematics, physics, and biology; Part V includes various extensions and generalizations of the Tutte polynomial; and Part VI provides a history of the development of the Tutte polynomial.
Features
- Written in an accessible style for non-experts, yet extensive enough for experts
- Serves as a comprehensive and accessible introduction to the theory of graph polynomials for researchers in mathematics, physics, and computer science
- Provides an extensive reference volume for the evaluations, theorems, and properties of the Tutte polynomial and related graph, matroid, and knot invariants
- Offers broad coverage, touching on the wide range of applications of the Tutte polynomial and its various specializations
商品描述(中文翻譯)
《Tutte 多項式》幾乎涉及組合數學的每個領域，以及許多其他領域，包括統計力學、編碼理論和 DNA 序列分析。它是最受研究的圖形多項式之一。
《Tutte 多項式及相關主題手冊》是第一本關於 Tutte 多項式的手冊。該手冊由該領域的專家撰寫，共有三十四章，集體提供了該多項式的許多性質和應用的簡明概述。每一章涵蓋 Tutte 多項式的不同方面，並包含該主題的核心結果和參考文獻。這些章節分為六個部分。第一部分描述了 Tutte 多項式的基本性質，提供了 Tutte 多項式的概述以及手冊其餘部分所需的背景知識。第二部分關注 Tutte 多項式的計算、複雜性和近似問題；第三部分涵蓋了一些相關的圖形多項式；第四部分討論了 Tutte 多項式在數學、物理和生物學中的一系列應用；第五部分包括 Tutte 多項式的各種擴展和概括；第六部分提供了 Tutte 多項式發展的歷史。
特色
- 以易於理解的風格撰寫，適合非專家，但對專家來說也足夠詳盡
- 為數學、物理和計算機科學的研究人員提供圖形多項式理論的全面且易於理解的介紹
- 提供 Tutte 多項式及相關圖形、矩陣和結的不變量的評估、定理和性質的廣泛參考資料
- 提供廣泛的涵蓋，觸及 Tutte 多項式及其各種專門化的廣泛應用
作者簡介
Joanna A. Ellis-Monaghan is a professor of discrete mathematics at the Korteweg - de Vries Instituut voor Wiskunde at the Universiteit van Amsterdam. Her research focuses on algebraic combinatorics, especially graph polynomials, as well as applications of combinatorics to DNA self-assembly, statistical mechanics, computer chip design, and bioinformatics. She also has an interest in mathematical pedagogy. She has published over 50 papers in these areas.
Iain Moffatt is a professor of mathematics in Royal Holloway, University of London. His main research interests lie in the interactions between topology and combinatorics. He is especially interested in graph polynomials, topological graph theory, matroid theory, and knot theory. He has written more than 40 papers in these areas and is also the author of the book An Introduction to Quantum and Vassiliev Knot invariants.
Ellis-Monaghan and Moffatt have authored several papers on the Tutte polynomial and related graph polynomials together as well as the book Graphs on surfaces: Dualities, Polynomials, and Knots.
作者簡介(中文翻譯)
喬安娜·艾莉斯-莫納漢是阿姆斯特丹大學科爾特維克-德弗里斯數學研究所的離散數學教授。她的研究專注於代數組合學，特別是圖多項式，以及組合學在DNA自組裝、統計力學、計算機晶片設計和生物資訊學中的應用。她也對數學教育學有興趣。她在這些領域已發表超過50篇論文。
伊恩·莫法特是倫敦皇家霍洛威大學的數學教授。他的主要研究興趣在於拓撲學與組合學之間的相互作用。他特別關注圖多項式、拓撲圖論、矩陣理論和結理論。他在這些領域撰寫了超過40篇論文，並且是書籍量子與瓦西里耶夫結不變量導論的作者。
艾莉斯-莫納漢和莫法特 共同撰寫了幾篇關於圖特多項式及相關圖多項式的論文，以及書籍曲面上的圖：對偶性、多項式與結。
