本书系统地介绍了与程序设计竞赛有关的组合数学的基本理论和算法设计与分析的常用方法。全书共分8章，分别为：算法基础、组合数学初探、排列与组合、容斥原理、母函数、拟阵、贪心算法和Pólya定理。本书突出组合数学算法的设计与优化，从而更便于参加程序设计竞赛的读者学习组合数学。 本书可作为ACM/ICPC国际大学生程序设计竞赛和国际信息学奥林匹在竞赛（IOI）的培训教材，也可供从事组合数学与算法研究的人员参考。

本书介绍组合数学中的基础理论和实际应用，讲述的内容非常广泛，讨论的问题涵盖组合数学所涉及的绝大部分领域。本书不仅包含了通常组合数学教科书中的经典内容，而且收集了若干新的内容，如Lovász筛法、范德瓦尔登积和式猜想、结合区组设计、码和设计等。 本书阐述深入浅出，简明易懂，适合作为高等院校高年级本科生与低年级研究生的组合数学课程教材，也适合作为数学和其他学科的研究人员的参考书。

Praise for the Second Edition : "Serious researchers in combinatorics or algorithm design will wish to read the book in its entirety...the book may also be enjoyed on a lighter level since the different chapters are largely independent and so it is possible to pick out gems in one's own area..." — Formal Aspects of Computing This Third Edition of The Probabilistic Method reflects the most recent developments in the field while maintaining the standard of excellence that established this book as the leading reference on probabilistic methods in combinatorics. Maintaining its clear writing style, illustrative examples, and practical exercises, this new edition emphasizes methodology, enabling readers to use probabilistic techniques for solving problems in such fields as theoretical computer science, mathematics, and statistical physics. The book begins with a description of tools applied in probabilistic arguments, including basic techniques that use expectation and variance as well as the more recent applications of martingales and correlation inequalities. Next, the authors examine where probabilistic techniques have been applied successfully, exploring such topics as discrepancy and random graphs, circuit complexity, computational geometry, and derandomization of randomized algorithms. Sections labeled "The Probabilistic Lens" offer additional insights into the application of the probabilistic approach, and the appendix has been updated to include methodologies for finding lower bounds for Large Deviations. The Third Edition also features: A new chapter on graph property testing, which is a current topic that incorporates combinatorial, probabilistic, and algorithmic techniques An elementary approach using probabilistic techniques to the powerful Szemerédi Regularity Lemma and its applications New sections devoted to percolation and liar games A new chapter that provides a modern treatment of the Erdös-Rényi phase transition in the Random Graph Process Written by two leading authorities in the field, The Probabilistic Method , Third Edition is an ideal reference for researchers in combinatorics and algorithm design who would like to better understand the use of probabilistic methods. The book's numerous exercises and examples also make it an excellent textbook for graduate-level courses in mathematics and computer science.

The leading reference on probabilistic methods in combinatorics-now expanded and updated When it was first published in 1991, The Probabilistic Method became instantly the standard reference on one of the most powerful and widely used tools in combinatorics. Still without competition nearly a decade later, this new edition brings you up to speed on recent developments, while adding useful exercises and over 30ew material. It continues to emphasize the basic elements of the methodology, discussing in a remarkably clear and informal style both algorithmic and classical methods as well as modern applications. The Probabilistic Method, Second Edition begins with basic techniques that use expectation and variance, as well as the more recent martingales and correlation inequalities, then explores areas where probabilistic techniques proved successful, including discrepancy and random graphs as well as cutting-edge topics in theoretical computer science. A series of proofs, or "probabilistic lenses," are interspersed throughout the book, offering added insight into the application of the probabilistic approach. New and revised coverage includes: * Several improved as well as new results * A continuous approach to discrete probabilistic problems * Talagrand's Inequality and other novel concentration results * A discussion of the connection between discrepancy and VC-dimension * Several combinatorial applications of the entropy function and its properties * A new section on the life and work of Paul Erdös-the developer of the probabilistic method

《组合数学》(原书第4版)侧重于组合数学的概念和思想，包括鸽巢原理、计数技术、排列组合、Polya计数法、二项式系数、容斥原理、生成函数和递推关系以及组合结构(匹配、实验设计、图)等，深入浅出地表达了作者对该领域全面和深刻的理解，介绍了历史上源于数学游戏和娱乐的大量实例，其中对Polya计数、Burnside定理等的完美处理使得不熟悉群论的学生也能够读懂。除包含第3版中的内容外，本版又进行了更新，增加了莫比乌斯反演(作为容斥原理的推广)、格路径、Schroder数等内容。此外，各章均包含大量练习题，并在书末给出了参考答案与提示。

组合数学，ISBN：9787302045816，作者：卢开澄，卢华明著