Enumerative Combinatorics: Volume 1
Enumerative Combinatorics: Volume 1
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发表时间：
2011-12
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通讯作者：
R. Stanley
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作者：
R. Stanley
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。第1卷的这个彻底修订的第二版包括10个新章节和300多个新练习，大多数都有解决方案，反映了自1986年第一版出版以来的许多新发展。第1卷的材料被选来涵盖列举组合学中最具适用性和与其他数学领域最重要联系的部分。这四章专门介绍枚举（适合高级本科生），筛选方法，部分有序集，有理生成函数。许多材料与生成函数有关，这是枚举组合学中的基本工具。在这个新的版本中，作者带来了最新的覆盖范围，包括各种各样的额外的应用程序和例子，以及更新和扩展的章节参考书目。许多难度较低的新练习都没有答案，这样就可以更容易地分配给学生。对p分区上的材料进行了重新整理和推广；排列统计的处理得到了极大的扩展；此外，还有关于置换的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 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.