计数组合学

内容概要

Richard P．Stanley现任麻省理工学院数学系教授、美国艺术与科学院院士、美国国家科学院院士。他是国际组合学界的领袖之一，曾获工业与应用数学学会授予的应用组合学的Pblya奖，并于2001年因本书获得美国数学学会Steele奖，2003年获得Schock奖。

书籍目录

Notation

Chapter 1 What Is Enumerative Combinatorics?

1.1 How to Count

1.2 Sets and Multisets

1.3 Permutation Statistics

1.4 The Twelvefold Way

Notes

References

A Note about the Exercises

Exercises

Solutions to Exercises

Chapter 2 Sieve Methods

2.1 Inclusion-Exclusion

2.2 Examples and Special Cases

2.3 Permutations with Restricted Positions

2.4 Ferrers Boards

2.5 V-partitions and Unimodal Sequences

2.6 Involutions

2.7 Determinants

Notes

References

Exercises

Solutions to Exercises

Chapter 3 Partially Ordered Sets

3.1 Basic Concepts

3.2 New Posets from Old

3.3 Lattices

3.4 Distributive Lattices

315 Chains in Distributive Lattices

3.6 The Incidence Algebra of a Locally Finite Poset

3.7 The MObius Inversion Formula

3.8 Techniques for Computing MObius Functions

3.9 Lattices and Their MObius Algebras

3.10 The MObius Function of a Semimodular Lattice

3.11 Zeta Polynomials

3.12 Rank-selection

3.13 R-labelings

3.14 Eulerian Posets

3.15 Binomial Posets and Generating Functions

3.16 An Application to Permutation Enumeration

Notes

References

Exercises

Solutions to Exercises

Chapter 4 Rational Generating Functions

4.1 Rational Power Series in One Variable

4.2 Further Ramifications

4.3 Polynomials

4.4 Quasi-polynomials

4.5 P-partitions

4.6 Linear Homogeneous Diophantine Equations

4.7 The Transfer-matrix Method

Notes

References

Exercises

Solutions to Exercises

Appendix Graph Theory Terminology

Index

Supplementary Problems

Errata and Addenda

作者简介

本书重点介绍生成函数的理论和应用，生成函数是计数组合学的基本工具。本书分四章介绍了计数、筛法、偏序集以及有理生成函数，并欢未包含在正文中的许多数学领域提供了入门知识。书中所选择的材料覆盖了计数组合学中应用范围最广以及与其他数学领域联系最密切的部分。另外，书中包含大量习题，并几乎对所有习题都提供了解答，有助于教学。

　　本书是两卷集计数组合学基础导论中的第1卷，适合于研究生和数学研究人员。

图书封面

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