Combinatorics (Fall 2010)
 | |
| Instructor | |
|---|---|
| 尹一通 | |
| yitong.yin@gmail.com yinyt@nju.edu.cn yinyt@lamda.nju.edu.cn | |
| office | 蒙民伟楼 406 |
| Class | |
| Class meetings |
10am -12am, Friday, 馆I-105 |
| Office hours | 2pm-5pm, Saturday, MMW 406 |
| Textbook | |
|
van Lint and Wilson, A course in Combinatorics, 2nd Ed, Cambridge Univ Press, 2001. | |
This is the page for the class Combinatorics for the Fall 2010 semester. Students who take this class should check this page periodically for content updates and new announcements.
Announcement
- (2010/11/04) 由于校运动会本科生停课，明天（11月5日）的课暂停。请同学们相互转告。
- (2010/10/26) 第八次课讲义已补完。
- (2010/10/29) 第三次作业已发布，11月12日课上交。
- (2010/10/26) 第七次课讲义已补完。
Course info
- Instructor : 尹一通
- email: yitong.yin@gmail.com, yinyt@nju.edu.cn, yinyt@lamda.nju.edu.cn
- office: MMW 406.
- Teaching fellow: 林木丰
- email: forest.sky.sea@gmail.com
- Class meeting: 10am-12 am, Friday; 馆I-105.
- Office hour: 2-5pm, Saturday; MMW 406.
Syllabus
先修课程 Prerequisites
- 离散数学（Discrete Mathematics）
- 线性代数（Linear Algebra）
- 概率论（Probability Theory）
Course materials
Policies
Assignments
- (2010/09/17) Problem set 1 due on Sept 25, in class.
- (2010/10/12) Solution
- (2010/10/15) Problem set 2 due on Oct 29, in class.
- (2010/10/29) Problem set 3 due on Nov 12, in class.
交作业名单
Lecture Notes
A tentative list of topics:
- Basic enumeration | slides
- Partitions, Sieve methods | slides
- Generating functions | slides
- Existence, the probabilistic method | slides
- Random graphs | slides
- Extremal graphs | slides
- Finite set systems | slides
- Extremal set theory | slides
- Extremal set theory II (under construction...)
- Ramsey theory (under construction...)
- Optimization
- Duality
- Flow and matching
- Matroid
- Spectra of graphs
- Harmonic analysis of boolean functions
- The Szemeredi regularity lemma
- Sum-product theorems, Kakeya set
Concepts
- Binomial coefficient
- Composition of a number
- Combinations with repetition, [math]\displaystyle{ k }[/math]-multisets on a set
- Stirling number of the second kind
- Partition of a number
- The twelvefold way
- Ferrers diagram (and the MathWorld link)
- The principle of inclusion-exclusion (and more generally the sieve method)
- Derangement, and Problème des ménages
- Generating function and formal power series
- Fibonacci number
- Newton's formula
- Catalan number
- Double counting and the handshaking lemma
- Cayley's formula
- Pigeonhole principle
- The Probabilistic Method
- Erdős–Rényi model for random graphs
- Graph property
- Some graph parameters: girth [math]\displaystyle{ g(G) }[/math], chromatic number [math]\displaystyle{ \chi(G) }[/math], Independence number [math]\displaystyle{ \alpha(G) }[/math], clique number [math]\displaystyle{ \omega(G) }[/math]
- Extremal graph theory
- Turán's theorem, Turán graph
- Two analytic inequalities:
- Erdős–Stone theorem (fundamental theorem of extremal graph theory)
- Dirac's theorem
- Hall's theorem (the marriage theorem)
- Birkhoff-Von Neumann theorem
- König-Egerváry theorem
- Dilworth's theorem
- Sperner system
- Erdős–Ko–Rado theorem
- VC dimension
- Kruskal–Katona theorem