计数组合学 卷1-2 21年度美国数学会Steele数学专著奖 MIT应用数学教授

基本信息

Series:Cambridge Studies in Advanced Mathematics

Format:约642 +788pages

Weight:约1110+1346g

Dimensions:234 x 163 x 44 (mm)/本

页面参数仅供参考，具体以实物为准

目录

9781107015425 计数组合学 卷一 21年度美国数学会Steele数学专著奖 MIT应用数学教授 Enumerative Combinatorics Volume 1

9781009262491 计数组合学 卷二 21年度美国数学会Steele数学专著奖 MIT应用数学教授 Enumerative Combinatorics Volume 2

系列简介

1、计数组合学 卷一 21年度美国数学会Steele数学专著奖 MIT应用数学教授 Enumerative Combinatorics Volume 1

理查德·斯坦利（Richard Stanley）的两卷本枚举组合学基础介绍已成为学生和专家的该主题的标准指南。 卷一的第二版经过彻底修订，包括 10 个新章节和 300 多个新练习，其中大部分带有解答，反映了自 1986 年一版出版以来的众多新发展。作者更新了内容，包括多种内容 其他应用程序和示例，以及更新和扩展的章节参考书目。

许多难度较低的新练习没有答案，因此可以更容易地分配给学生。 有关 P 分区的材料已重新整理和概括； 排列统计的处理已大大扩展； 还有关于排列的 q 类似物、超平面排列、CD 索引、提升和疏散以及微分偏序集的新章节。

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 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.

2、计数组合学 卷二 21年度美国数学会Steele数学专著奖 MIT应用数学教授 Enumerative Combinatorics Volume 2

理查德·斯坦利（Richard Stanley）的两卷本枚举组合学基础介绍已成为学生和专家的该主题的标准指南。 第二卷的第二版经过彻底修订，涵盖了生成函数的组成，特别是指数公式和拉格朗日反演公式、标记和未标记树、代数、D-有限和非交换生成函数以及对称函数。 关于对称函数的章节提供了该主题的可用处理方法，适合研究生入门课程，重点关注组合学，特别是 Robinson-Schensted-Knuth 算法。

Sergey Fomin 的附录涵盖了对称函数的一些更深层次的方面，包括 jeu de taquin 和 Littlewood-Richardson 规则。 书中的练习在教材的编写中发挥着至关重要的作用，第二版包含 400 多个练习，其中包括 159 个关于对称函数的新练习，所有练习都带有解决方案或解决方案的参考。

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 two covers the composition of generating functions, in particular the exponential formula and the Lagrange inversion formula, labelled and unlabelled trees, algebraic, D-finite, and noncommutative generating functions, and symmetric functions. The chapter on symmetric functions provides the available treatment of this subject suitable for an introductory graduate course and focusing on combinatorics, especially the Robinson–Schensted–Knuth algorithm.

An appendix by Sergey Fomin covers some deeper aspects of symmetric functions, including jeu de taquin and the Littlewood–Richardson rule. The exercises in the book play a vital role in developing the material, and this second edition features over 400 exercises, including 159 new exercises on symmetric functions, all with solutions or references to solutions.

作者简介

理查德·P·斯坦利 (Richard P. Stanley) 是麻省理工学院应用数学教授。 他被公认为组合学及其在各种其他数学学科中的应用领域的领先专家。 除了开创性的两卷本《枚举组合学》之外，他还是《组合学和交换代数》(1983) 以及 100 多篇数学研究文章的作者。 Stanley 获得的众多荣誉包括美国国家科学院院士（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.