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

基本信息

Series:Cambridge Studies in Advanced Mathematics

Format: 788 pages, Worked examples or Exercises

Publisher:Cambridge University Press

Imprint:Cambridge University Press

Edition:2 Revised edition

ISBN:9781009262491

Published:17 Aug 2023

Weight:1346g

Dimensions:161 x 242 x 56 (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（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) 是麻省理工学院数学名誉教授，也是迈阿密大学艺术与科学杰出教授。 他撰写了 180 多篇研究文章和六本书。 Stanley 获得的众多荣誉包括美国国家科学院院士（1995 年当选）和 2001 年 Leroy P. Steele 数学博览会奖。

Richard P. Stanley is Emeritus Professor of Mathematics at the Massachusetts Institute of Technology and an Arts and Sciences Distinguished Professor at the University of Miami. He has written over 180 research articles and six books. Among Stanley's many distinctions are membership in the National Academy of Sciences (elected in 1995) and the 2001 Leroy P. Steele Prize for Mathematical Exposition.