User contributions for Etone

17 June 2026

• 04:0504:05, 17 June 2026 diff hist +34,076 N 组合数学 (Fall 2026)/Matching theory Created page with "== Systems of Distinct Representatives (SDR)== A '''system of distinct representatives (SDR)''' (also called a '''transversal''') for a sequence of (not necessarily distinct) sets <math>S_1,S_2,\ldots,S_m</math> is a sequence of <font color=red>''distinct''</font> elements <math>x_1,x_2,\ldots,x_m</math> such that <math>x_i\in S_i</math> for all <math>i=1,2,\ldots,m</math>. === Hall's marriage theorem === If the sets <math>S_1,S_2,\ldots,S_m</math> have a system of dist..." current
• 04:0404:04, 17 June 2026 diff hist +141 组合数学 (Spring 2026) →Lecture Notes current

20 May 2026

• 13:3313:33, 20 May 2026 diff hist +26,029 N 组合数学 (Fall 2026)/Ramsey theory Created page with "== Ramsey's Theorem == === Ramsey's theorem for graph === {{Theorem|Ramsey's Theorem| :Let <math>k,\ell</math> be positive integers. Then there exists an integer <math>R(k,\ell)</math> satisfying: :If <math>n\ge R(k,\ell)</math>, for any coloring of edges of <math>K_n</math> with two colors red and blue, there exists a red <math>K_k</math> or a blue <math>K_\ell</math>. }} {{Proof| We show that <math>R(k,\ell)</math> is finite by induction on <math>k+\ell</math>. For the..." current
• 13:3213:32, 20 May 2026 diff hist +137 组合数学 (Spring 2026) →Lecture Notes

13 May 2026

• 08:4908:49, 13 May 2026 diff hist +51,460 N 组合数学 (Fall 2026)/Extremal set theory Created page with "== Sunflowers == An set system is a '''sunflower''' if all its member sets intersect at the same set of elements. {{Theorem|Definition (sunflower)| : A set family <math>\mathcal{F}\subseteq 2^X</math> is a '''sunflower''' of size <math>r</math> with a '''core''' <math>C\subseteq X</math> if ::<math>\forall S,T\in\mathcal{F}</math> that <math>S\neq T</math>, <math>S\cap T=C</math>. }} Note that we do not require the core to be nonempty, thus a family of disjoint sets is..." current
• 08:4808:48, 13 May 2026 diff hist +13 组合数学 (Spring 2026) →Lecture Notes
• 08:4608:46, 13 May 2026 diff hist +475 组合数学 (Spring 2026) →Lecture Notes
• 08:4208:42, 13 May 2026 diff hist 0 组合数学 (Spring 2026) →Lecture Notes

6 May 2026

• 05:0105:01, 6 May 2026 diff hist +18,939 N 组合数学 (Fall 2026)/Extremal graph theory Created page with "== Forbidden Cliques == Extremal graph theory studies the problems like "how many edges that a graph <math>G</math> can have, if <math>G</math> has some property?" === Mantel's theorem === We consider a typical extremal problem for graphs: the largest possible number of edges of '''triangle-free''' graphs, i.e. graphs contains no <math>K_3</math>. {{Theorem|Theorem (Mantel 1907)| :Suppose <math>G(V,E)</math> is graph on <math>n</math> vertice without triangles. Then <m..." current
• 05:0005:00, 6 May 2026 diff hist +158 组合数学 (Spring 2026) →Lecture Notes

17 April 2026

• 13:1813:18, 17 April 2026 diff hist +27,151 N 组合数学 (Fall 2026)/The probabilistic method Created page with "== The Probabilistic Method == The probabilistic method provides another way of proving the existence of objects: instead of explicitly constructing an object, we define a probability space of objects in which the probability is positive that a randomly selected object has the required property. The basic principle of the probabilistic method is very simple, and can be stated in intuitive ways: *If an object chosen randomly from a universe satisfies a property with posi..." current
• 13:1813:18, 17 April 2026 diff hist 0 组合数学 (Spring 2026) →Lecture Notes
• 13:1713:17, 17 April 2026 diff hist +157 组合数学 (Spring 2026) →Lecture Notes

16 April 2026

• 08:1308:13, 16 April 2026 diff hist +5,139 N 概率论与数理统计 (Spring 2026)/Weierstrass Approximation Theorem Created page with "[https://en.wikipedia.org/wiki/Stone%E2%80%93Weierstrass_theorem '''魏尔施特拉斯逼近定理''']（'''Weierstrass approximation theorem'''）陈述了这样一个事实：闭区间上的连续函数总可以用多项式一致逼近。 {{Theorem|魏尔施特拉斯逼近定理| :设 <math>f:[a,b]\to\mathbb{R}</math> 为定义在实数区间 <math>[a,b]</math> 上的连续实值函数。对每个 <math>\epsilon>0</math>，存在一个多项式 <math>p</math> 使得对..." current
• 08:1208:12, 16 April 2026 diff hist +7,005 N 概率论与数理统计 (Spring 2026)/Threshold of k-clique in random graph Created page with "在 Erdős-Rényi 随机图模型 <math>G(n,p)</math> 中，一个随机无向图 <math>G</math> 以如下的方式生成：图 <math>G</math> 包含 <math>n</math> 个顶点，每一对顶点之间都独立同地以概率 <math>p</math> 连一条无向边。如此生成的随机图记为 <math>G\sim G(n,p)</math>。 固定整数 <math>k\ge 3</math>，考虑随机图 <math>G\sim G(n,p)</math> 包含 <math>K_k</math>（<math>k</math>-团，<math>k</math>-clique）子图..." current
• 08:1208:12, 16 April 2026 diff hist +430 概率论与数理统计 (Spring 2026) →Lectures

8 April 2026

• 08:5908:59, 8 April 2026 diff hist +14,440 N 组合数学 (Fall 2026)/Existence problems Created page with "== Existence by Counting == === Shannon's circuit lower bound=== This is a fundamental problem in in Computer Science. A '''boolean function''' is a function in the form <math>f:\{0,1\}^n\rightarrow \{0,1\}</math>. [http://en.wikipedia.org/wiki/Boolean_circuit Boolean circuit] is a mathematical model of computation. Formally, a boolean circuit is a directed acyclic graph. Nodes with indegree zero are input nodes, labeled <math>x_1, x_2, \ldots , x_n</math>. A circuit h..." current
• 08:5908:59, 8 April 2026 diff hist +87 组合数学 (Spring 2026) →Lecture Notes
• 08:5408:54, 8 April 2026 diff hist +8 组合数学 (Spring 2026) →Lecture Notes
• 08:5208:52, 8 April 2026 diff hist +114 组合数学 (Spring 2026) →Lecture Notes
• 08:4508:45, 8 April 2026 diff hist +17,231 N 组合数学 (Fall 2026)/Cayley's formula Created page with "== Cayley's Formula == We now present a theorem of the number of labeled trees on a fixed number of vertices. It is due to [http://en.wikipedia.org/wiki/Arthur_Cayley Cayley] in 1889. The theorem is often referred by the name [http://en.wikipedia.org/wiki/Cayley's_formula Cayley's formula]. {{Theorem|Cayley's formula for trees| : There are <math>n^{n-2}</math> different trees on <math>n</math> distinct vertices. }} The theorem has several proofs, including the bijectio..." current
• 08:4008:40, 8 April 2026 diff hist +141 组合数学 (Spring 2026) →Lecture Notes
• 08:3808:38, 8 April 2026 diff hist +11,838 N 概率论与数理统计 (Spring 2026)/Average-case analysis of QuickSort Created page with "[http://en.wikipedia.org/wiki/Quicksort '''快速排序'''（'''Quicksort'''）]是由Tony Hoare发现的排序算法。该算法的伪代码描述如下（为方便起见，假设数组元素互不相同——更一般情况的分析易推广得到）： '''''QSort'''''(A): 输入A[1...n]是存有n个不同数字的数组 if n>1 then '''pivot''' = A[1]; 将A中<pivot的元素存于数组L，将A中>pivot的元素存于数组R; \\保持内部元素之..." current
• 08:3808:38, 8 April 2026 diff hist +126 概率论与数理统计 (Spring 2026) →Lectures

30 March 2026

• 17:2117:21, 30 March 2026 diff hist +33,970 N 组合数学 (Fall 2026)/Sieve methods Created page with "== Principle of Inclusion-Exclusion == Let <math>A</math> and <math>B</math> be two finite sets. The cardinality of their union is :<math>|A\cup B|=|A|+|B|-{\color{Blue}|A\cap B|}</math>. For three sets <math>A</math>, <math>B</math>, and <math>C</math>, the cardinality of the union of these three sets is computed as :<math>|A\cup B\cup C|=|A|+|B|+|C|-{\color{Blue}|A\cap B|}-{\color{Blue}|A\cap C|}-{\color{Blue}|B\cap C|}+{\color{Red}|A\cap B\cap C|}</math>. This is illu..." current
• 17:2017:20, 30 March 2026 diff hist +125 组合数学 (Spring 2026) →Lecture Notes
• 17:1917:19, 30 March 2026 diff hist +12,035 N 概率论与数理统计 (Spring 2026)/Karger's min-cut algorithm Created page with "令 <math>G(V, E)</math> 是一个无向图。我们称边集 <math>C\subseteq E</math> 是图 <math>G</math> 的一个'''割'''，如果图 <math>G</math> 在删除所有 <math>C</math> 中的边后变得不连通。 '''最小割问题''', 也称为'''全局最小割问题''', 定义如下。 {{Theorem|全局最小割问题| *'''输入'''：无向图 <math>G(V,E)</math>； *'''输出'''：图 <math>G</math> 中具有最小 <math>|C|</math> 的割 <math>C</math>。 }}..." current
• 17:1817:18, 30 March 2026 diff hist +179 概率论与数理统计 (Spring 2026) →Lectures
• 17:1717:17, 30 March 2026 diff hist +101 概率论与数理统计 (Spring 2026) →Lectures

17 March 2026

• 09:4109:41, 17 March 2026 diff hist +3,052 N 概率论与数理统计 (Spring 2026)/Entropy and volume of Hamming balls Created page with "在求解抛掷公平硬币（fair coin）的尾概率时，我们经常会需要分析如下二项式系数求和： :<math>\sum_{k=0}^r{n\choose k}</math>，对于某个<math>1\le r\le n</math> 这其实等价与求一个 <math>n</math> 维汉明空间中半径为 <math>r</math> 的球的体积。 :{|border="2" width="100%" cellspacing="4" cellpadding="3" rules="all" style="margin:1em 1em 1em 0; border:solid 1px #AAAAAA; border-collapse:collapse;empty-cells:show;" | :'..." current
• 09:4009:40, 17 March 2026 diff hist +118 概率论与数理统计 (Spring 2026) →Lectures

11 March 2026

• 08:5108:51, 11 March 2026 diff hist +1 组合数学 (Spring 2026) →Lecture Notes
• 08:5108:51, 11 March 2026 diff hist +71 组合数学 (Spring 2026) →Lecture Notes
• 08:3808:38, 11 March 2026 diff hist +25,549 N 组合数学 (Spring 2026)/Generating functions Created page with "== Generating Functions == In Stanley's magnificent book ''Enumerative Combinatorics'', he comments the generating function as "the most useful but most difficult to understand method (for counting)". The solution to a counting problem is usually represented as some <math>a_n</math> depending a parameter <math>n</math>. Sometimes this <math>a_n</math> is called a ''counting function'' as it is a function of the parameter <math>n</math>. <math>a_n</math> can also be tre..." current
• 08:3708:37, 11 March 2026 diff hist +90 组合数学 (Spring 2026) →Lecture Notes

9 March 2026

• 08:5908:59, 9 March 2026 diff hist +70 组合数学 (Spring 2026) →Lecture Notes
• 08:5708:57, 9 March 2026 diff hist +190 概率论与数理统计 (Spring 2026) →Lectures

3 March 2026

• 08:5808:58, 3 March 2026 diff hist +39,712 N 组合数学 (Spring 2026)/Basic enumeration Created page with "== Basic Enumeration == The three basic rules for enumeration are: *'''The sum rule''': for any '''''disjoint''''' finite sets <math>S</math> and <math>T</math>, the cardinality of the union <math>|S\cup T|=|S|+|T|</math>. *'''The product rule''': for any finite sets <math>S</math> and <math>T</math>, the cardinality of the Cartesian product <math>|S\times T|=|S|\cdot|T|</math>. *'''The bijection rule''': if there exists a bijection between finite sets <math>S</math> a..." current
• 08:5708:57, 3 March 2026 diff hist +81 组合数学 (Spring 2026) →Lecture Notes
• 08:5608:56, 3 March 2026 diff hist +10,239 N 组合数学 (Spring 2026) Created page with "{{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=..."
• 07:4707:47, 3 March 2026 diff hist +76 Main Page →Home Pages for Courses and Seminars
• 07:4507:45, 3 March 2026 diff hist −37 Main Page No edit summary

30 November 2025

• 09:4309:43, 30 November 2025 diff hist +2,459 N Assignment 4, Fall 2025 Created page with "在第四章中，我们从准地转近似下的纬向平均风场、温度场的趋势方程出发，定义了E-P通量。但是该定义下的E-P通量并没有考虑到大气湿过程的影响。如果从第三章介绍的水汽方程出发，我们可以按照以下步骤定义出一个包含大气大尺度运动中湿过程作用的广义的E-P通量。 1）在准地转近似下，如果我们按照对热力学方程的简化方法，将比湿（specific humidity..." current
• 09:4209:42, 30 November 2025 diff hist +70 General Circulation(Fall 2025) →Assignments current

26 October 2025

• 15:0015:00, 26 October 2025 diff hist +1,087 N Assignment 3, Fall 2025 Created page with "Held-Hou(1980) 讨论了当外部强迫的经向分布呈二次勒让德多项式，即<math>\dfrac{\Theta_E(\phi,z)}{\Theta_o}=1-\dfrac{2}{3}\Delta_H P_2(\sin \phi)+\Delta_v(\dfrac{z}{H}-\dfrac{1}{2})</math>的情况下，哈德莱环流内的风场、温度场、环流的空间范围等将怎样随纬度和外力强迫的强度而变化。如果将外力强迫的空间分布改为<math>\dfrac{\Theta_E(\phi,z)}{\Theta_o}=1-\Delta_H(\sin \phi -\frac{1}{2})+\Delta_v(\dfra..." current
• 14:5914:59, 26 October 2025 diff hist +59 General Circulation(Fall 2025) →Assignments

20 October 2025

• 02:2202:22, 20 October 2025 diff hist +6 Namelist Assignment 1 2025 No edit summary current
• 02:2202:22, 20 October 2025 diff hist +1,184 N Namelist Assignment 1 2025 Created page with "学号 姓名 221830009 丁潘宇 221840131 崔亚川 221830192 张梓轩 221830060 梁茗豪 221840001 檀纯芳 221840042 刘鑫磊 221840183 胡峻滔 221840252 徐玘 221830079 余秀蓝 221840217 于步涵 221840063 樊瑾奕 221840226 郑凯容 221840163 周若冰 221840204 张利荣 652025280008 李俊霖 502025280011 苟敏杰 502025280051 吴雨涵 502024280014 何昌霖 502025280038 齐若彤 502025280008 冯英飞 502025280022 蒋妍 50202..."
• 02:0802:08, 20 October 2025 diff hist +55 General Circulation(Fall 2025) →Assignments

16 October 2025

• 04:1804:18, 16 October 2025 diff hist 0 高级算法 (Fall 2025) →Lecture Notes Tag: Manual revert