组合数学 (Spring 2013): Difference between revisions

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|data11  = '' <br> A course in Combinatorics, 2nd ed.'', <br> van Lint and Wilson, <br> Cambridge Univ Press, 2001.
|data11  = van Lint and Wilson. <br> ''A course in Combinatorics, 2nd ed.'', <br> Cambridge Univ Press, 2001.
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|data13  = ''Extremal Combinatorics: <br> With Applications in Computer Science,<br>2nd ed.'', Jukna, Springer, 2011.
|data13  = Jukna. ''Extremal Combinatorics: <br> With Applications in Computer Science,<br>2nd ed.'', Springer, 2011.
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= Announcement =
= 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 =
= Course info =
Line 65: Line 69:
:*email: yitong.yin@gmail.com, yinyt@nju.edu.cn,
:*email: yitong.yin@gmail.com, yinyt@nju.edu.cn,
:*office: 804
:*office: 804
* '''Teaching fellow''': TBA
* '''Teaching fellow''': 金宇
:*email: TBA
:*email: jinyu1122@hotmail.com
* '''Class meeting''': Thursday 8am-10am, 仙 I-103.
* '''Class meeting''': Thursday 8am-10am, 仙 I-103.
* '''Office hour''': Wednesday 2-4pm, 计算机系 804.
* '''Office hour''': Wednesday 2-4pm, 计算机系 804.


= Syllabus =
= Syllabus =
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=== 成绩 Grades ===
=== 成绩 Grades ===
* 课程成绩:本课程将会有六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。
* 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。
* 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。


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= Assignments =
= 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 =
= Lecture Notes =
# [[组合数学 (Spring 2013)/Basic enumeration|Basic enumeration]]  
# [[组合数学 (Spring 2013)/Basic enumeration|Basic enumeration]] | [http://tcs.nju.edu.cn/slides/comb2013/comb1.pdf slides1] | [http://tcs.nju.edu.cn/slides/comb2013/comb2-1.pdf slides2]  
# Generating functions  
# [[组合数学 (Spring 2013)/Generating functions|Generating functions]] | [http://tcs.nju.edu.cn/slides/comb2013/comb2-2.pdf slides1] | [http://tcs.nju.edu.cn/slides/comb2013/comb3.pdf slides2] 
# Sieve methods
# [[组合数学 (Spring 2013)/Sieve methods|Sieve methods]] | [http://tcs.nju.edu.cn/slides/comb2013/comb4.pdf slides1] | [http://tcs.nju.edu.cn/slides/comb2013/comb5-1.pdf slides2]
# Pólya's theory of counting
# [[组合数学 (Spring 2013)/Cayley's formula|Cayley's formula]] | [http://tcs.nju.edu.cn/slides/comb2013/comb5-2.pdf slides]
# Counting and existence
#  [[组合数学 (Spring 2013)/Pólya's theory of counting|Pólya's theory of counting]] | [http://tcs.nju.edu.cn/slides/comb2013/comb6.pdf slides1] | [http://tcs.nju.edu.cn/slides/comb2013/comb7-1.pdf slides2] 
# The probabilistic method
# [[组合数学 (Spring 2013)/Existence problems|Existence problems]] | [http://tcs.nju.edu.cn/slides/comb2013/comb7-2.pdf slides1] | [http://tcs.nju.edu.cn/slides/comb2013/comb8-1.pdf slides2] 
# Extremal graph theory
# [[组合数学 (Spring 2013)/The probabilistic method|The probabilistic method]] | [http://tcs.nju.edu.cn/slides/comb2013/comb9.pdf slides] 
# Extremal set theory
# [[组合数学 (Spring 2013)/Extremal graph theory|Extremal graph theory]] | [http://tcs.nju.edu.cn/slides/comb2013/comb10.pdf slides1] | [http://tcs.nju.edu.cn/slides/comb2013/comb11-1.pdf slides2] 
# Ramsey theory
# [[组合数学 (Spring 2013)/Extremal set theory|Extremal set theory]] | [http://tcs.nju.edu.cn/slides/comb2013/comb11-2.pdf slides1] | [http://tcs.nju.edu.cn/slides/comb2013/comb12.pdf slides2]   
# Matching theory
# [[组合数学 (Spring 2013)/Ramsey theory|Ramsey theory]] | [http://tcs.nju.edu.cn/slides/comb2013/comb13.pdf slides] 
# Flow and matching
# [[组合数学 (Spring 2013)/Matching theory| Matching theory]] | [http://tcs.nju.edu.cn/slides/comb2013/comb14.pdf slides] 
# [[组合数学 (Spring 2013)/Flow and matching|Flow and matching]] | [http://tcs.nju.edu.cn/slides/comb2013/comb15.pdf slides]


= Concepts =
= 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]

Latest revision as of 12:46, 15 September 2017

组合数学
Combinatorics
Instructor
尹一通
Email yitong.yin@gmail.com yinyt@nju.edu.cn
office 计算机系 804
Class
Class meetings Thursday, 8am-10am
仙 I-103
Office hours Wednesday, 2-4pm
计算机系 804
Textbook
van Lint and Wilson.
A course in Combinatorics, 2nd ed.,
Cambridge Univ Press, 2001.
Jukna. Extremal Combinatorics:
With Applications in Computer Science,
2nd ed.
, Springer, 2011.
v · d · e

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

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

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。

学术诚信 Academic Integrity

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 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, 抄袭和被抄袭双方的成绩都将被取消。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

Lecture Notes

  1. Basic enumeration | slides1 | slides2
  2. Generating functions | slides1 | slides2
  3. Sieve methods | slides1 | slides2
  4. Cayley's formula | slides
  5. Pólya's theory of counting | slides1 | slides2
  6. Existence problems | slides1 | slides2
  7. The probabilistic method | slides
  8. Extremal graph theory | slides1 | slides2
  9. Extremal set theory | slides1 | slides2
  10. Ramsey theory | slides
  11. Matching theory | slides
  12. Flow and matching | slides

Concepts