Enumerative Combinatorics

Richard Stanley
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Abstract

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 only 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.
列举的组合
理查德·斯坦利(Richard Stanley)的两卷本枚举组合学基本介绍已经成为学生和专家的标准指南。这个彻底修订的第二卷第二版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这个主题的唯一可用的处理方法,适合于研究生入门课程,并专注于组合学,特别是罗宾逊-申斯泰德-高努算法。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。书中的练习在发展材料中起着至关重要的作用,这第二版有超过400个练习,包括159个关于对称函数的新练习,所有的解决方案或参考解决方案。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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