计算组合 卷一（剑桥高等数学研究系列）（麻省理工数学荣誉退休教授）第二版 Enumerative Combinatorics: Volume 1

基本信息

Series:Cambridge Studies in Advanced Mathematics

Format:Paperback / softback 642 pages, Worked examples or Exercises; 165 Line drawings, unspecified

Publisher:Cambridge University Press

Imprint:Cambridge University Press

Edition:2 Revised edition

ISBN:9781107602625

Published:12 Dec 2011

Weight:940g

Dimensions:225 x 154 x 35 (mm)

页面参数仅供参考，具体以实物为准

书籍简介

理查德-斯坦利的两卷本《计算组合》已经成为学生和专家对该主题的标准指南。第一卷的第二版经过彻底修订，包括10个新的章节和300多个新的练习题，其中大部分有解答，反映了自1986年第一版出版以来的许多新发展。第1卷中的材料被选择来涵盖列举组合学中适用性强的部分，以及与其他数学领域重要的联系。四章专门介绍了枚举法（适合高级本科生）、筛子方法、部分有序集和有理生成函数。许多材料与生成函数有关，生成函数是枚举组合学的一个基本工具。在这个新版本中，作者将内容更新，并包括各种额外的应用和例子，以及更新和扩大的章节参考书目。许多难度较低的新习题没有答案，这样可以更容易地分配给学生。关于P-分区的材料已被重新安排和概括；对互换统计的处理已大大增加；还有关于互换的q-类似物、超平面排列、CD-指数、促进和疏散以及微分位置集的新章节。

Richard Stanley's two-volume basic introduction to enumerative combinatorics has become the standard guide to the topic for students and experts alike. This thoroughly revised second edition of Volume 1 includes ten new sections and more than 300 new exercises, most with solutions, reflecting numerous new developments since the publication of the first edition in 1986. The material in Volume 1 was chosen to cover those parts of enumerative combinatorics of greatest applicability and with the most important connections with other areas of mathematics. The four chapters are devoted to an introduction to enumeration (suitable for advanced undergraduates), sieve methods, partially ordered sets, and rational generating functions. Much of the material is related to generating functions, a fundamental tool in enumerative combinatorics. In this new edition, the author brings the coverage up to date and includes a wide variety of additional applications and examples, as well as updated and expanded chapter bibliographies. Many of the less difficult new exercises have no solutions so that they can more easily be assigned to students. The material on P-partitions has been rearranged and generalized; the treatment of permutation statistics has been greatly enlarged; and there are also new sections on q-analogues of permutations, hyperplane arrangements, the cd-index, promotion and evacuation, and differential posets.

作者简介

Richard P. Stanley是美国麻省理工学院的应用数学教授。他被公认为是组合学领域及其在其他各种数学学科中应用的主要专家。除了两卷本的开创性著作《计算组合》外，他还是《组合学与共轭代数》（1983年）以及100多篇数学研究文章的作者。在斯坦利的众多荣誉中，包括国家科学院院士（1995年当选）、2001年Leroy P. Steele数学阐述奖和2003年Schock奖。

Richard P. Stanley is a Professor of Applied Mathematics at the Massachusetts Institute of Technology. He is universally recognized as a leading expert in the field of combinatorics and its applications to a variety of other mathematical disciplines. In addition to the seminal two-volume book Enumerative Combinatorics, he is the author of Combinatorics and Commutative Algebra (1983) as well as more than 100 research articles in mathematics. Among Stanley's many distinctions are membership in the National Academy of Sciences (elected in 1995), the 2001 Leroy P. Steele Prize for mathematical exposition and the 2003 Schock Prize.