Combinatorics (Fall 2010): Difference between revisions
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# [[Combinatorics (Fall 2010)/Extremal graphs| Extremal graphs]] | [http://lamda.nju.edu.cn/yinyt/notes/comb2010/comb6.pdf slides] | # [[Combinatorics (Fall 2010)/Extremal graphs| Extremal graphs]] | [http://lamda.nju.edu.cn/yinyt/notes/comb2010/comb6.pdf slides] | ||
# [[Combinatorics (Fall 2010)/Finite set systems|Finite set systems]] | # [[Combinatorics (Fall 2010)/Finite set systems|Finite set systems]] | ||
# Extremal set theory | # [[Combinatorics (Fall 2010)/Extremal set theory|Extremal set theory]] | ||
# Ramsey theory | # Ramsey theory | ||
# Optimization | # Optimization |
Revision as of 01:33, 18 October 2010
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
- (2010/10/17) 第六次课讲义已补完。
- (2010/10/15) 第二次作业已发布,10月29日课上交。
- (2010/10/13) 第一次作业答案已公布,见assignment部分。
- (2010/10/12) 第五次课讲义已补完。
- (2010/10/02) 第四次课讲义已补完, 讲义最后附有参考阅读的章节.
- (2010/09/27) 第一次交作业的名单已公布,见assignment。如果交了作业但没有看到名字,请与我联系。
- (2010/09/24) 提醒:明天(9月25日)上课时交作业。
- (2010/09/15) 第一次作业已发布,9月25日课上交。
- (2010/09/15) 第二课的lecture notes和slides中有个错误,
- [math]\displaystyle{ |U|-\sum_{I\subseteq\{1,\ldots,n\}}(-1)^{|I|}\left|\bigcap_{i\in I}A_i\right| }[/math] 的正负号有误,应为 [math]\displaystyle{ |U|+\sum_{I\subseteq\{1,\ldots,n\}}(-1)^{|I|}\left|\bigcap_{i\in I}A_i\right| }[/math] 或 [math]\displaystyle{ |U|-\sum_{I\subseteq\{1,\ldots,n\}}(-1)^{|I|-1}\left|\bigcap_{i\in I}A_i\right| }[/math]。
- 感谢林文敏同学发现这个错误。
- (2010/09/11) 前两节课slides已上传,在lecture notes的部分有链接。
- 9月3日第一次课。时间:上午三、四节;地点:馆I-105。
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.
交作业名单
- (2010/09/27) 第一次交作业名单
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
- Extremal set theory
- Ramsey theory
- 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
- Erdős–Stone theorem (fundamental theorem of extremal graph theory)
- Dirac's theorem