Combinatorics: Notes and Problem Set

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一些有趣的组合应用问题

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计数组合

排列与组合

1. 概述

   • 计数组合学的记号和基本概念

2. [基本计数模型和公式]

3. 习题集

   • 随手做的一个问题

抽屉原理

1. 抽屉原理

2. [Ramsey 原理]

3. 习题集

   • 最长单调子序列问题

   • Pigeonhole Principle Exercise 001

   • Pigeonhole Principle Exercise 002

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生成排列与组合算法

1. [逆序数与生成排列]

2. [生成幂集与 r-子集]

3. [其他类型集合的生成算法]

4. 习题集

偏序集

1. 偏序集引论

2. Mirsky’s and Dilworth’s theorem

3. Sperner Theorem

4. 习题集

二项式系数与二项式定理

1. [二项式系数]

2. [二项式定理与性质]

3. [二项式定理的推广]

4. 习题集

容斥原理

1. 容斥原理

2. [莫比乌斯反演]

3. 习题集

递推关系和生成函数

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特殊计数序列

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组合设计

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图论

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