View source for 组合数学 (Spring 2013)

{{Infobox
|name         = Infobox
|bodystyle    = 
|title        = <font size=3>组合数学  <br>
Combinatorics</font>
|titlestyle   = 

|image        = 
|imagestyle   = 
|caption      = 
|captionstyle = 
|headerstyle  = background:#ccf;
|labelstyle   = background:#ddf;
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|header1 =Instructor
|label1  = 
|data1   = 
|header2 = 
|label2  = 
|data2   = 尹一通
|header3 = 
|label3  = Email
|data3   = yitong.yin@gmail.com  yinyt@nju.edu.cn  
|header4 =
|label4= office
|data4= 计算机系 804
|header5 = Class
|label5  = 
|data5   = 
|header6 =
|label6  = Class meetings
|data6   = Thursday, 8am-10am <br> 仙 I-103
|header7 =
|label7  = Place
|data7   = 
|header8 =
|label8  = Office hours
|data8   = Wednesday, 2-4pm <br>计算机系 804
|header9 = Textbook
|label9  = 
|data9   = 
|header10 =
|label10  = 
|data10   = [[File:LW-combinatorics.jpeg|border|100px]]
|header11 =
|label11  = 
|data11   = van Lint and Wilson. <br> ''A course in Combinatorics, 2nd ed.'', <br> Cambridge Univ Press, 2001.
|header12 =
|label12  = 
|data12   = [[File:Jukna_book.jpg|border|100px]]
|header13 =
|label13  = 
|data13   = Jukna. ''Extremal Combinatorics: <br> With Applications in Computer Science,<br>2nd ed.'', Springer, 2011.
|belowstyle = background:#ddf;
|below = 
}}

This is the page for the class ''Combinatorics'' for the Spring 2013 semester. Students who take this class should check this page periodically for content updates and new announcements. 

= Announcement =
*  <font size=4 color=red>The third [[组合数学 (Spring 2013)/Problem_Set_3|homework assignment]] is out, due in two weeks. </font>
*  The second [[组合数学 (Spring 2013)/Problem_Set_2|homework assignment]] is out, due inONE week. 
* 由于清明假期，作业提交时间推迟一周（4月11日课上交）。
*  The first [[组合数学 (Spring 2013)/Problem_Set_1|homework assignment]] is out, due in two weeks.

= Course info =
* '''Instructor ''': 尹一通
:*email: yitong.yin@gmail.com, yinyt@nju.edu.cn,
:*office: 804
* '''Teaching fellow''': 金宇
:*email: jinyu1122@hotmail.com
* '''Class meeting''': Thursday 8am-10am, 仙 I-103.
* '''Office hour''': Wednesday 2-4pm, 计算机系 804.

= 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 ===
* [[组合数学 (Spring 2013)/Course materials|<font size=3>教材和参考书清单</font>]]

=== 成绩 Grades ===
* 课程成绩：本课程将会有若干次作业和一次期末考试。最终成绩将由平时作业成绩和期末考试成绩综合得出。
* 迟交：如果有特殊的理由，无法按时完成作业，请提前联系授课老师，给出正当理由。否则迟交的作业将不被接受。

=== <font color=red> 学术诚信 Academic Integrity </font>===
学术诚信是所有从事学术活动的学生和学者最基本的职业道德底线，本课程将不遗余力的维护学术诚信规范，违反这一底线的行为将不会被容忍。

作业完成的原则：'''署你名字的工作必须由你完成'''。允许讨论，但作业必须独立完成，并在作业中列出所有参与讨论的人。不允许其他任何形式的合作——尤其是与已经完成作业的同学“讨论”。

本课程将对剽窃行为采取零容忍的态度。在完成作业过程中，对他人工作（出版物、互联网资料、其他人的作业等）直接的文本抄袭和对关键思想、关键元素的抄袭，按照 [http://www.acm.org/publications/policies/plagiarism_policy ACM Policy on Plagiarism]的解释，都将视为剽窃。剽窃者成绩将被取消。如果发现互相抄袭行为，<font color=red> 抄袭和被抄袭双方的成绩都将被取消</font>。因此请主动防止自己的作业被他人抄袭。

学术诚信影响学生个人的品行，也关乎整个教育系统的正常运转。为了一点分数而做出学术不端的行为，不仅使自己沦为一个欺骗者，也使他人的诚实努力失去意义。让我们一起努力维护一个诚信的环境。

= Assignments =
*[[组合数学 (Spring 2013)/Problem Set 1|Problem Set 1]], due on April 4, Thursday, in class.
*[[组合数学 (Spring 2013)/Problem Set 2|Problem Set 2]], due on April 25, Thursday, in class.
*[[组合数学 (Spring 2013)/Problem Set 3|Problem Set 3]], due on May 23, Thursday, in class.
*[[组合数学 (Spring 2013)/Problem Set 4|Problem Set 4]], due on June 20, Thursday, in class.

= Lecture Notes =
# [[组合数学 (Spring 2013)/Basic enumeration|Basic enumeration]] | [ftp://tcs.nju.edu.cn/slides/comb2013/comb1.pdf slides1] | [ftp://tcs.nju.edu.cn/slides/comb2013/comb2-1.pdf slides2] 
# [[组合数学 (Spring 2013)/Generating functions|Generating functions]] | [ftp://tcs.nju.edu.cn/slides/comb2013/comb2-2.pdf slides1] | [ftp://tcs.nju.edu.cn/slides/comb2013/comb3.pdf slides2]  
# [[组合数学 (Spring 2013)/Sieve methods|Sieve methods]] | [ftp://tcs.nju.edu.cn/slides/comb2013/comb4.pdf slides1] | [ftp://tcs.nju.edu.cn/slides/comb2013/comb5-1.pdf slides2] 
#  [[组合数学 (Spring 2013)/Cayley's formula|Cayley's formula]] | [ftp://tcs.nju.edu.cn/slides/comb2013/comb5-2.pdf slides] 
#  [[组合数学 (Spring 2013)/Pólya's theory of counting|Pólya's theory of counting]] | [ftp://tcs.nju.edu.cn/slides/comb2013/comb6.pdf slides1] | [ftp://tcs.nju.edu.cn/slides/comb2013/comb7-1.pdf slides2]  
#  [[组合数学 (Spring 2013)/Existence problems|Existence problems]] | [ftp://tcs.nju.edu.cn/slides/comb2013/comb7-2.pdf slides1]  
#  [[组合数学 (Spring 2013)/The probabilistic method|The probabilistic method]]
#  [[组合数学 (Spring 2013)/Extremal graph theory|Extremal graph theory]]
#  [[组合数学 (Spring 2013)/Extremal set theory|Extremal set theory]]
#  [[组合数学 (Spring 2013)/Ramsey theory|Ramsey theory]]
#  [[组合数学 (Spring 2013)/Matching theory| Matching theory]]
#  [[组合数学 (Spring 2013)/Flow and matching|Flow and matching]]

= Concepts =
* [http://en.wikipedia.org/wiki/Binomial_coefficient Binomial coefficient]
* [http://en.wikipedia.org/wiki/Composition_(number_theory) Composition of a number]
* [http://en.wikipedia.org/wiki/Combination#Number_of_combinations_with_repetition Combinations with repetition], [http://en.wikipedia.org/wiki/Multiset_coefficient#Multiset_coefficients <math>k</math>-multisets on a set]
* [http://en.wikipedia.org/wiki/Stirling_numbers_of_the_second_kind Stirling number of the second kind]
* [http://en.wikipedia.org/wiki/Partition_(number_theory) Partition of a number]
* [http://en.wikipedia.org/wiki/Partition_(number_theory)#Ferrers_diagram Ferrers diagram] (and the MathWorld [http://mathworld.wolfram.com/FerrersDiagram.html link])
* [http://en.wikipedia.org/wiki/Twelvefold_way The twelvefold way]
* [http://en.wikipedia.org/wiki/Generating_function Generating function] and [http://en.wikipedia.org/wiki/Formal_power_series formal power series]
* [http://en.wikipedia.org/wiki/Fibonacci_number Fibonacci number]
* [http://en.wikipedia.org/wiki/Binomial_series Newton's formula]
* [http://en.wikipedia.org/wiki/Catalan_number Catalan number]
* [http://en.wikipedia.org/wiki/Inclusion-exclusion_principle The principle of inclusion-exclusion] (and more generally the [http://en.wikipedia.org/wiki/Sieve_theory sieve method])
* [http://en.wikipedia.org/wiki/M%C3%B6bius_inversion_formula Möbius inversion formula]
* [http://en.wikipedia.org/wiki/Derangement Derangement], and [http://en.wikipedia.org/wiki/M%C3%A9nage_problem Problème des ménages]
* [http://en.wikipedia.org/wiki/Ryser%27s_formula#Ryser_formula Ryser's formula]
* [http://en.wikipedia.org/wiki/Euler_totient Euler totient function]
* [http://en.wikipedia.org/wiki/Cayley_formula Cayley's formula]
** [http://en.wikipedia.org/wiki/Prüfer_sequence Prüfer code for trees]
** [http://en.wikipedia.org/wiki/Kirchhoff%27s_matrix_tree_theorem Kirchhoff's matrix-tree theorem]
* [http://en.wikipedia.org/wiki/Double_counting_(proof_technique) Double counting] and the [http://en.wikipedia.org/wiki/Handshaking_lemma handshaking lemma]
* [http://en.wikipedia.org/wiki/Sperner's_lemma Sperner's lemma] and [http://en.wikipedia.org/wiki/Brouwer_fixed_point_theorem Brouwer fixed point theorem]
* [http://en.wikipedia.org/wiki/Pigeonhole_principle Pigeonhole principle]
:* [http://en.wikipedia.org/wiki/Erd%C5%91s%E2%80%93Szekeres_theorem Erdős–Szekeres theorem]
:* [http://en.wikipedia.org/wiki/Dirichlet's_approximation_theorem Dirichlet's approximation theorem]
* [http://en.wikipedia.org/wiki/Probabilistic_method The Probabilistic Method]
* [http://en.wikipedia.org/wiki/Lov%C3%A1sz_local_lemma Lovász local lemma]
* [http://en.wikipedia.org/wiki/Erd%C5%91s%E2%80%93R%C3%A9nyi_model Erdős–Rényi model for random graphs]
* [http://en.wikipedia.org/wiki/Extremal_graph_theory Extremal graph theory]
* [http://en.wikipedia.org/wiki/Turan_theorem Turán's theorem], [http://en.wikipedia.org/wiki/Tur%C3%A1n_graph Turán graph]
* Two analytic inequalities: 
:*[http://en.wikipedia.org/wiki/Cauchy%E2%80%93Schwarz_inequality Cauchy–Schwarz inequality]
:* the [http://en.wikipedia.org/wiki/Inequality_of_arithmetic_and_geometric_means inequality of arithmetic and geometric means]
* [http://en.wikipedia.org/wiki/Erd%C5%91s%E2%80%93Stone_theorem Erdős–Stone theorem] (fundamental theorem of extremal graph theory)
* [http://en.wikipedia.org/wiki/Sperner_family Sperner system]
* [http://en.wikipedia.org/wiki/Erd%C5%91s%E2%80%93Ko%E2%80%93Rado_theorem Erdős–Ko–Rado theorem]
* [http://en.wikipedia.org/wiki/Ramsey_theory Ramsey theory]
:*[http://en.wikipedia.org/wiki/Ramsey's_theorem Ramsey's theorem]
:*[http://en.wikipedia.org/wiki/Happy_Ending_problem Happy Ending problem]
* [http://en.wikipedia.org/wiki/Hall's_theorem Hall's theorem ] (the marriage theorem)
* [http://en.wikipedia.org/wiki/K%C3%B6nig's_theorem_(graph_theory) König-Egerváry theorem]
* [http://en.wikipedia.org/wiki/Dilworth's_theorem Dilworth's theorem]
* The  [http://en.wikipedia.org/wiki/Max-flow_min-cut_theorem Max-Flow Min-Cut Theorem]
:* [http://en.wikipedia.org/wiki/Maximum_flow_problem Maximum flow]
* [http://en.wikipedia.org/wiki/Linear_programming Linear programming]
* [http://en.wikipedia.org/wiki/Dual_linear_program Duality]
:* [http://en.wikipedia.org/wiki/Linear_programming#Duality LP Duality]
* [http://en.wikipedia.org/wiki/Unimodular_matrix Unimodularity]