TCS Wiki - User contributions [en]

计算复杂性 (Spring 2026)

2026-04-21T10:45:44Z

Roundgod: /* Assignments */

组合数学 (Spring 2024)

2026-03-09T04:06:51Z

Roundgod: /* removed slides for assignment in combinatorics spring 2024 */

{{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;
|datastyle =

|header1 =Instructor
|label1 =
|data1 =
|header2 =
|label2 =
|data2 = 尹一通
|header3 =
|label3 = Email
|data3 = yinyt@nju.edu.cn
|header4 =
|label4= office
|data4= 计算机系 804
|header5 = Class
|label5 =
|data5 =
|header6 =
|label6 = Class meetings
|data6 = Wednesday, 2pm-4pm <br> 仙Ⅱ-211
|header7 =
|label7 = Place
|data7 =
|header8 =
|label8 = Office hours
|data8 = TBA <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 webpage for the ''Combinatorics'' class of Spring 2024. Students who take this class should check this page periodically for content updates and new announcements.

= Announcement =
* '''(2024/03/19)'''<font color=red size=4> 第一次作业已发布</font>，请在 2024/04/03 上课之前提交到 [mailto:njucomb24@163.com njucomb24@163.com] (文件名为'学号_姓名_A1.pdf').
* '''(2024/04/10)'''<font color=red size=4> 第二次作业已发布</font>，请在 2024/04/24 上课之前提交到 [mailto:njucomb24@163.com njucomb24@163.com] (文件名为'学号_姓名_A2.pdf').
* '''(2024/05/15)'''<font color=red size=4> 第三次作业已发布</font>，请在 2024/05/29 上课之前提交到 [mailto:njucomb24@163.com njucomb24@163.com] (文件名为'学号_姓名_A3.pdf').
* '''(2024/06/04)'''<font color=red size=4> 第四次作业已发布</font>，请在 2024/06/16 习题课之前提交到 [mailto:njucomb24@163.com njucomb24@163.com] (文件名为'学号_姓名_A4.pdf').
* '''(2024/06/12)'''<font color=red size=4> 本周日（6月16日）上习题课</font>，下午14:00-16:00，地点在逸C-105。
* '''(2024/06/19)'''<font color=red size=4> 习题课slides已经上传</font>。

= Course info =
* '''Instructor ''': 尹一通 ([http://tcs.nju.edu.cn/yinyt/ homepage])
:*'''email''': yinyt@nju.edu.cn
:*'''office''': 计算机系 804
* '''Teaching assistant''':
** [https://lhy-gispzjz.github.io 刘弘洋] ([mailto:liuhongyang@smail.nju.edu.cn liuhongyang@smail.nju.edu.cn])
** [https://wcysai.com 王淳扬] ([mailto:wcysai@smail.nju.edu.cn wcysai@smail.nju.edu.cn])
* '''Class meeting''': Wednesday, 2pm-4pm, 仙Ⅱ-211.
* '''Office hour''': TBA
:* '''QQ群''': 709281027 (加入时需报姓名、专业、学号)

= 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 2024)/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 (≥ 60%) 和期末考试成绩 (≤ 40%) 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是你个人的贡献。在完成作业的过程中，允许讨论，前提是讨论的所有参与者均处于同等完成度。但关键想法的执行、以及作业文本的写作必须独立完成，并在作业中致谢（acknowledge）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 2024)/Problem Set 1|Problem Set 1]] [[组合数学 (Spring 2024)/第一次作业提交名单|第一次作业提交名单]]
* [[组合数学 (Spring 2024)/Problem Set 2|Problem Set 2]] [[组合数学 (Spring 2024)/第二次作业提交名单|第二次作业提交名单]]
* [[组合数学 (Spring 2024)/Problem Set 3|Problem Set 3]] [[组合数学 (Spring 2024)/第三次作业提交名单|第三次作业提交名单]]
* [[组合数学 (Spring 2024)/Problem Set 4|Problem Set 4]] [[组合数学 (Spring 2024)/第四次作业提交名单|第四次作业提交名单]]

= Lecture Notes =
# [[组合数学 (Fall 2024)/Basic enumeration|Basic enumeration | 基本计数]] ([http://tcs.nju.edu.cn/slides/comb2024/BasicEnumeration.pdf slides])
# [[组合数学 (Fall 2024)/Generating functions|Generating functions | 生成函数]] ([http://tcs.nju.edu.cn/slides/comb2024/GeneratingFunction.pdf slides])
# [[组合数学 (Fall 2024)/Sieve methods|Sieve methods | 筛法]] ([http://tcs.nju.edu.cn/slides/comb2024/PIE.pdf slides])
# [[组合数学 (Fall 2024)/Pólya's theory of counting|Pólya's theory of counting | Pólya计数法]] ([http://tcs.nju.edu.cn/slides/comb2024/Polya.pdf slides])
# [[组合数学 (Fall 2024)/Cayley's formula|Cayley's formula | Cayley公式]] ([http://tcs.nju.edu.cn/slides/comb2024/Cayley.pdf slides])
# [[组合数学 (Fall 2024)/Existence problems|Existence problems | 存在性问题]] ([http://tcs.nju.edu.cn/slides/comb2024/Existence.pdf slides])
# [[组合数学 (Fall 2024)/The probabilistic method|The probabilistic method | 概率法]] ([http://tcs.nju.edu.cn/slides/comb2024/ProbMethod.pdf slides])
# [[组合数学 (Fall 2024)/Extremal graph theory|Extremal graph theory | 极值图论]] ([http://tcs.nju.edu.cn/slides/comb2024/ExtremalGraphs.pdf slides])
# [[组合数学 (Fall 2024)/Extremal set theory|Extremal set theory | 极值集合论]]（[http://tcs.nju.edu.cn/slides/comb2024/ExtremalSets.pdf slides]）
#* [https://mathweb.ucsd.edu/~ronspubs/90_03_erdos_ko_rado.pdf Old and new proofs of the Erdős–Ko–Rado theorem] by Frankl and Graham
#* [https://arxiv.org/pdf/1908.08483.pdf Improved bounds for the sunflower lemma] by Alweiss-Lovet-Wu-Zhang and a [https://arxiv.org/pdf/1909.04774.pdf simplified proof] by Rao
# [[组合数学 (Fall 2024)/Ramsey theory|Ramsey theory | Ramsey理论]]（[http://tcs.nju.edu.cn/slides/comb2024/Ramsey.pdf slides]）
# [[组合数学 (Fall 2024)/Matching theory|Matching theory | 匹配论]]（[http://tcs.nju.edu.cn/slides/comb2024/Matchings.pdf slides]）

= Resources =
* [http://math.mit.edu/~fox/MAT307.html Combinatorics course] by Jacob Fox
* [https://yufeizhao.com/pm/ Probabilistic Methods in Combinatorics] and [https://yufeizhao.com/gtacbook/ Graph Theory and Additive Combinatorics] by Yufei Zhao
* [https://www.math.uvic.ca/~noelj/combinatoricsLectures.html Combinatorics Lecture Videos online]
* [https://www.math.ucla.edu/~pak/lectures/Math-Videos/comb-videos.htm Collection of Combinatorics Videos]

= Concepts =
* [http://en.wikipedia.org/wiki/Binomial_coefficient Binomial coefficient]
* [http://en.wikipedia.org/wiki/Twelvefold_way The twelvefold way]
* [http://en.wikipedia.org/wiki/Composition_(number_theory) Composition of a number]
* [http://en.wikipedia.org/wiki/Multiset#Formal_definition Multiset]
* [http://en.wikipedia.org/wiki/Combination#Number_of_combinations_with_repetition Combinations with repetition], [http://en.wikipedia.org/wiki/Multiset#Counting_multisets <math>k</math>-multisets on a set]
* [http://en.wikipedia.org/wiki/Multinomial_theorem#Multinomial_coefficients Multinomial coefficients]
* [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/Young_tableau Young tableau]
* [http://en.wikipedia.org/wiki/Fibonacci_number Fibonacci number]
* [http://en.wikipedia.org/wiki/Catalan_number Catalan number]
* [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/Binomial_series Newton's formula]
* [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]
* [https://en.wikipedia.org/wiki/Burnside%27s_lemma Burnside's lemma]
** [https://en.wikipedia.org/wiki/Group_action Group action]
** [https://en.wikipedia.org/wiki/Group_action#Orbits_and_stabilizers Orbits]
* [https://en.wikipedia.org/wiki/P%C3%B3lya_enumeration_theorem Pólya enumeration theorem]
** [https://en.wikipedia.org/wiki/Permutation_group Permutation group]
** [https://en.wikipedia.org/wiki/Cycle_index Cycle index]
* [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)
* [https://en.wikipedia.org/wiki/Sunflower_(mathematics) Sunflower lemma and conjecture]
* [https://en.wikipedia.org/wiki/Erd%C5%91s%E2%80%93Ko%E2%80%93Rado_theorem Erdős–Ko–Rado theorem]
* [https://en.wikipedia.org/wiki/Sperner%27s_theorem Sperner's theorem]
** [https://en.wikipedia.org/wiki/Sperner_family Sperner system] or '''antichain'''
* [https://en.wikipedia.org/wiki/Sauer%E2%80%93Shelah_lemma Sauer–Shelah lemma]
** [https://en.wikipedia.org/wiki/Vapnik%E2%80%93Chervonenkis_dimension Vapnik–Chervonenkis dimension]
* [https://en.wikipedia.org/wiki/Kruskal%E2%80%93Katona_theorem Kruskal–Katona 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]
:*[https://en.wikipedia.org/wiki/Van_der_Waerden%27s_theorem Van der Waerden's theorem]
:*[https://en.wikipedia.org/wiki/Hales%E2%80%93Jewett_theorem Hales–Jewett theorem]
* [https://en.wikipedia.org/wiki/Hall%27s_marriage_theorem Hall's theorem ] (the marriage theorem)
:* [https://en.wikipedia.org/wiki/Doubly_stochastic_matrix Birkhoff–Von Neumann 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]
:* [http://en.wikipedia.org/wiki/Erd%C5%91s%E2%80%93Szekeres_theorem Erdős–Szekeres theorem]
* The [http://en.wikipedia.org/wiki/Max-flow_min-cut_theorem Max-Flow Min-Cut Theorem]
:* [https://en.wikipedia.org/wiki/Menger%27s_theorem Menger's theorem]
:* [http://en.wikipedia.org/wiki/Maximum_flow_problem Maximum flow]
* [https://en.wikipedia.org/wiki/Linear_programming Linear programming]
** [https://en.wikipedia.org/wiki/Dual_linear_program Duality]
** [https://en.wikipedia.org/wiki/Unimodular_matrix Unimodularity]
* [https://en.wikipedia.org/wiki/Matroid Matroid]

计算复杂性 (Spring 2026)

2026-03-02T10:25:47Z

Roundgod: 修改教室

File:Computational complexity.jpg

2026-03-02T05:36:46Z

Roundgod:

计算复杂性 (Spring 2026)

2026-03-02T05:35:53Z

Roundgod:

File:Computaional complexity.jpg

2024-06-03T11:43:31Z

Roundgod: /* Assignments */

{{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;
|datastyle =

|header1 =Instructor
|label1 =
|data1 =
|header2 =
|label2 =
|data2 = 尹一通
|header3 =
|label3 = Email
|data3 = yinyt@nju.edu.cn
|header4 =
|label4= office
|data4= 计算机系 804
|header5 = Class
|label5 =
|data5 =
|header6 =
|label6 = Class meetings
|data6 = Wednesday, 2pm-4pm <br> 仙Ⅱ-211
|header7 =
|label7 = Place
|data7 =
|header8 =
|label8 = Office hours
|data8 = TBA <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 webpage for the ''Combinatorics'' class of Spring 2024. Students who take this class should check this page periodically for content updates and new announcements.

= Announcement =
* '''(2024/03/19)'''<font color=red size=4> 第一次作业已发布</font>，请在 2024/04/03 上课之前提交到 [mailto:njucomb24@163.com njucomb24@163.com] (文件名为'学号_姓名_A1.pdf').
* '''(2024/04/10)'''<font color=red size=4> 第二次作业已发布</font>，请在 2024/04/24 上课之前提交到 [mailto:njucomb24@163.com njucomb24@163.com] (文件名为'学号_姓名_A2.pdf').
* '''(2024/05/15)'''<font color=red size=4> 第三次作业已发布</font>，请在 2024/05/29 上课之前提交到 [mailto:njucomb24@163.com njucomb24@163.com] (文件名为'学号_姓名_A3.pdf').

= Course info =
* '''Instructor ''': 尹一通 ([http://tcs.nju.edu.cn/yinyt/ homepage])
:*'''email''': yinyt@nju.edu.cn
:*'''office''': 计算机系 804
* '''Teaching assistant''':
** [https://lhy-gispzjz.github.io 刘弘洋] ([mailto:liuhongyang@smail.nju.edu.cn liuhongyang@smail.nju.edu.cn])
** [https://wcysai.com 王淳扬] ([mailto:wcysai@smail.nju.edu.cn wcysai@smail.nju.edu.cn])
* '''Class meeting''': Wednesday, 2pm-4pm, 仙Ⅱ-211.
* '''Office hour''': TBA
:* '''QQ群''': 709281027 (加入时需报姓名、专业、学号)

= 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 2024)/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 (≥ 60%) 和期末考试成绩 (≤ 40%) 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是你个人的贡献。在完成作业的过程中，允许讨论，前提是讨论的所有参与者均处于同等完成度。但关键想法的执行、以及作业文本的写作必须独立完成，并在作业中致谢（acknowledge）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 2024)/Problem Set 1|Problem Set 1]] [[组合数学 (Spring 2024)/第一次作业提交名单|第一次作业提交名单]]
* [[组合数学 (Spring 2024)/Problem Set 2|Problem Set 2]] [[组合数学 (Spring 2024)/第二次作业提交名单|第二次作业提交名单]]
* [[组合数学 (Spring 2024)/Problem Set 3|Problem Set 3]] [[组合数学 (Spring 2024)/第三次作业提交名单|第三次作业提交名单]]

= Lecture Notes =
# [[组合数学 (Fall 2024)/Basic enumeration|Basic enumeration | 基本计数]] ([http://tcs.nju.edu.cn/slides/comb2024/BasicEnumeration.pdf slides])
# [[组合数学 (Fall 2024)/Generating functions|Generating functions | 生成函数]] ([http://tcs.nju.edu.cn/slides/comb2024/GeneratingFunction.pdf slides])
# [[组合数学 (Fall 2024)/Sieve methods|Sieve methods | 筛法]] ([http://tcs.nju.edu.cn/slides/comb2024/PIE.pdf slides])
# [[组合数学 (Fall 2024)/Pólya's theory of counting|Pólya's theory of counting | Pólya计数法]] ([http://tcs.nju.edu.cn/slides/comb2024/Polya.pdf slides])
# [[组合数学 (Fall 2024)/Cayley's formula|Cayley's formula | Cayley公式]] ([http://tcs.nju.edu.cn/slides/comb2024/Cayley.pdf slides])
# [[组合数学 (Fall 2024)/Existence problems|Existence problems | 存在性问题]] ([http://tcs.nju.edu.cn/slides/comb2024/Existence.pdf slides])
# [[组合数学 (Fall 2024)/The probabilistic method|The probabilistic method | 概率法]] ([http://tcs.nju.edu.cn/slides/comb2024/ProbMethod.pdf slides])
# [[组合数学 (Fall 2024)/Extremal graph theory|Extremal graph theory | 极值图论]] ([http://tcs.nju.edu.cn/slides/comb2024/ExtremalGraphs.pdf slides])
# [[组合数学 (Fall 2024)/Extremal set theory|Extremal set theory | 极值集合论]]（[http://tcs.nju.edu.cn/slides/comb2024/ExtremalSets.pdf slides]）
#* [https://mathweb.ucsd.edu/~ronspubs/90_03_erdos_ko_rado.pdf Old and new proofs of the Erdős–Ko–Rado theorem] by Frankl and Graham
#* [https://arxiv.org/pdf/1908.08483.pdf Improved bounds for the sunflower lemma] by Alweiss-Lovet-Wu-Zhang and a [https://arxiv.org/pdf/1909.04774.pdf simplified proof] by Rao
# [[组合数学 (Fall 2024)/Ramsey theory|Ramsey theory | Ramsey理论]]（[http://tcs.nju.edu.cn/slides/comb2024/Ramsey.pdf slides]）

= Resources =
* [http://math.mit.edu/~fox/MAT307.html Combinatorics course] by Jacob Fox
* [https://yufeizhao.com/pm/ Probabilistic Methods in Combinatorics] and [https://yufeizhao.com/gtacbook/ Graph Theory and Additive Combinatorics] by Yufei Zhao
* [https://www.math.uvic.ca/~noelj/combinatoricsLectures.html Combinatorics Lecture Videos online]
* [https://www.math.ucla.edu/~pak/lectures/Math-Videos/comb-videos.htm Collection of Combinatorics Videos]

= Concepts =
* [http://en.wikipedia.org/wiki/Binomial_coefficient Binomial coefficient]
* [http://en.wikipedia.org/wiki/Twelvefold_way The twelvefold way]
* [http://en.wikipedia.org/wiki/Composition_(number_theory) Composition of a number]
* [http://en.wikipedia.org/wiki/Multiset#Formal_definition Multiset]
* [http://en.wikipedia.org/wiki/Combination#Number_of_combinations_with_repetition Combinations with repetition], [http://en.wikipedia.org/wiki/Multiset#Counting_multisets <math>k</math>-multisets on a set]
* [http://en.wikipedia.org/wiki/Multinomial_theorem#Multinomial_coefficients Multinomial coefficients]
* [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/Young_tableau Young tableau]
* [http://en.wikipedia.org/wiki/Fibonacci_number Fibonacci number]
* [http://en.wikipedia.org/wiki/Catalan_number Catalan number]
* [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/Binomial_series Newton's formula]
* [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]
* [https://en.wikipedia.org/wiki/Burnside%27s_lemma Burnside's lemma]
** [https://en.wikipedia.org/wiki/Group_action Group action]
** [https://en.wikipedia.org/wiki/Group_action#Orbits_and_stabilizers Orbits]
* [https://en.wikipedia.org/wiki/P%C3%B3lya_enumeration_theorem Pólya enumeration theorem]
** [https://en.wikipedia.org/wiki/Permutation_group Permutation group]
** [https://en.wikipedia.org/wiki/Cycle_index Cycle index]
* [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)
* [https://en.wikipedia.org/wiki/Sunflower_(mathematics) Sunflower lemma and conjecture]
* [https://en.wikipedia.org/wiki/Erd%C5%91s%E2%80%93Ko%E2%80%93Rado_theorem Erdős–Ko–Rado theorem]
* [https://en.wikipedia.org/wiki/Sperner%27s_theorem Sperner's theorem]
** [https://en.wikipedia.org/wiki/Sperner_family Sperner system] or '''antichain'''
* [https://en.wikipedia.org/wiki/Sauer%E2%80%93Shelah_lemma Sauer–Shelah lemma]
** [https://en.wikipedia.org/wiki/Vapnik%E2%80%93Chervonenkis_dimension Vapnik–Chervonenkis dimension]
* [https://en.wikipedia.org/wiki/Kruskal%E2%80%93Katona_theorem Kruskal–Katona 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]
:*[https://en.wikipedia.org/wiki/Van_der_Waerden%27s_theorem Van der Waerden's theorem]
:*[https://en.wikipedia.org/wiki/Hales%E2%80%93Jewett_theorem Hales–Jewett theorem]
* [https://en.wikipedia.org/wiki/Hall%27s_marriage_theorem Hall's theorem ] (the marriage theorem)
:* [https://en.wikipedia.org/wiki/Doubly_stochastic_matrix Birkhoff–Von Neumann 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]
:* [http://en.wikipedia.org/wiki/Erd%C5%91s%E2%80%93Szekeres_theorem Erdős–Szekeres theorem]
* The [http://en.wikipedia.org/wiki/Max-flow_min-cut_theorem Max-Flow Min-Cut Theorem]
:* [https://en.wikipedia.org/wiki/Menger%27s_theorem Menger's theorem]
:* [http://en.wikipedia.org/wiki/Maximum_flow_problem Maximum flow]
* [https://en.wikipedia.org/wiki/Linear_programming Linear programming]
** [https://en.wikipedia.org/wiki/Dual_linear_program Duality]
** [https://en.wikipedia.org/wiki/Unimodular_matrix Unimodularity]
* [https://en.wikipedia.org/wiki/Matroid Matroid]