Handbook of the Tutte Polynomial and Related Topics

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.

• 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

Tutte多項式涉及幾乎所有組合學領域，以及許多其他領域，包括統計力學、編碼理論和DNA序列。它是最研究的圖多項式之一。

《Tutte多項式及相關主題手冊》是第一本關於Tutte多項式的手冊。它由該領域的專家撰寫的34章組成，共同提供了該多項式的許多性質和應用的簡明概述。每一章節都涵蓋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，為手冊的其餘部分提供了概述和必要的背景知識。第二部分涉及Tutte多項式的計算、複雜度和近似問題；第三部分涵蓋了一些相關的圖多項式；第四部分討論了Tutte多項式在數學、物理和生物學中的各種應用；第五部分包括Tutte多項式的各種擴展和推廣；第六部分提供了Tutte多項式的發展歷史。

特點：
- 以易於理解的風格撰寫，適合非專家閱讀，同時也涵蓋了專家所需的廣泛內容。
- 為數學、物理和計算機科學研究人員提供了圖多項式理論的全面且易於理解的介紹。
- 提供了Tutte多項式及相關圖、體系和結的評估、定理和性質的廣泛參考資料。
- 涵蓋範圍廣泛，觸及Tutte多項式及其各種特殊化的廣泛應用。

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.

Joanna A. Ellis-Monaghan是阿姆斯特丹大學Korteweg - de Vries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、電腦芯片設計和生物信息學方面的應用。她還對數學教學方法有興趣。她在這些領域發表了50多篇論文。

Iain Moffatt是倫敦大學皇家霍洛威學院的數學教授。他的主要研究興趣在於拓撲學和組合學之間的相互作用。他尤其關注圖多項式、拓撲圖論、拟陣理論和結糸理論。他在這些領域撰寫了40多篇論文，並且是書籍《量子和瓦西里耶夫結糸不變量入門》的作者。

Ellis-Monaghan和Moffatt共同撰寫了幾篇關於Tutte多項式和相關圖多項式的論文，並合著了書籍《圖形在曲面上：對偶性、多項式和結糸》。