Main public logs

Combined display of all available logs of TCS Wiki. You can narrow down the view by selecting a log type, the username (case-sensitive), or the affected page (also case-sensitive).

• 03:28, 9 April 2025 Gispzjz talk contribs created page 组合数学 (Spring 2025)/Problem Set 2 (Created page with "== Problem 1 == Let <math>0\leq l\leq k\leq n</math>. Show that <math>\binom{n}{k}\binom{k}{l} = \binom{n}{l}\binom{n-l}{k-l}</math>. == Problem 2 == Prove the following claims related to Cayley's formula: * The number of rooted labelled forests with <math>n</math> vertices is given by <math>(n+1)^{n-1}</math>. * The number of unrooted labelled forests with <math>n</math> vertices and <math>k</math> connected components such that <math>1,\dots,k</math> belong to disti...")
• 06:36, 7 April 2025 Gispzjz talk contribs created page 组合数学 (Spring 2025)/第一次作业提交名单 (Created page with "如有错漏请邮件联系助教. <center> {| class="wikitable" |- ! 学号 !! 姓名 |- | 211220166 || 王诚昊 |- | 221180133 || 黄可唯 |- | 221220002 || 沈均文 |- | 221220029 || 陈俊翰 |- | 221220034 || 王旭 |- | 221220052 || 周宇轩 |- | 221220104 || 刘宇平 |- | 221220109 || 肖琰 |- | 221220111 || 于源智 |- | 221220123 || 董立伟 |- | 221240035 || 李想 |- | 221240065 || 何俊渊 |- | 221240073 || 李恒济 |- | 221300016 ||...")
• 03:56, 5 April 2025 Zouzongrui talk contribs created page 概率论与数理统计 (Spring 2025)/Problem Set 3 (Created page with "*每道题目的解答都要有完整的解题过程，中英文不限。 *我们推荐大家使用LaTeX, markdown等对作业进行排版。 == Assumption throughout Problem Set 3== <p>Without further notice, we are working on probability space <math>(\Omega,\mathcal{F},\mathbf{Pr})</math>.</p> <p>Without further notice, we assume that the expectation of random variables are well-defined.</p> <p>The term <math>\log</math> used in this context refers to the natural l...")
• 10:38, 2 April 2025 Liumingmou talk contribs uploaded a new version of File:高级算法（2025） Hashing.pdf
• 10:35, 2 April 2025 Liumingmou talk contribs created page File:高级算法（2025） Hashing.pdf
• 10:35, 2 April 2025 Liumingmou talk contribs uploaded File:高级算法（2025） Hashing.pdf
• 05:08, 2 April 2025 Houzhe talk contribs created page 计算方法 Numerical method (Spring 2025)/Homework3 提交名单 (Created page with "<center> {| class="wikitable" |- ! 学号 !! 姓名 |- | 221220090 || 周思桥 |- | 221240002 || 季悦宁 |- | 221240040 || 郑雯琪 |- | 231098068 || 戎昱 |- | 231098091 || 刘棣文 |- | 231098166 || 陈展 |- | 231200035 || 葛翰飞 |- | 231220006 || 陆华均 |- | 231220036 || 周楚函 |- | 231220049 || 张泽宇 |- | 231220065 || 劳汉显 |- | 231220067 || 黄裕书琪 |- | 231220071 || 吴江涛 |- | 231220122 || 安琦煜 |- | 231220132 ||...")
• 02:40, 2 April 2025 Kvrmnks talk contribs created page File:Computational Method 2025 Assignments 4.pdf
• 02:40, 2 April 2025 Kvrmnks talk contribs uploaded File:Computational Method 2025 Assignments 4.pdf
• 10:33, 1 April 2025 Etone talk contribs created page 概率论与数理统计 (Spring 2025)/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...")
• 10:33, 1 April 2025 Etone talk contribs created page 概率论与数理统计 (Spring 2025)/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...")
• 10:32, 1 April 2025 Etone talk contribs created page 概率论与数理统计 (Spring 2025)/Two-point sampling (Created page with "= 利用线性同余方程构造两两独立的随机变量 = 令<math>p</math>为一质数。考虑模<math>p</math>余数构成的集合<math>[p]=\{0,1,\ldots,p-1\}=\mathbb{Z}_p</math>。众所周知，当<math>p</math>为质数时，<math>\mathbb{Z}_p</math>为对模<math>p</math>加法和乘法运算闭合的'''有限域'''。 我们现在构造一系列值域为<math>[p]</math>的'''两两独立'''（'''pairwise Independent'''）且'''均匀分布'''（'''uniforml...")
• 07:23, 31 March 2025 Zouzongrui talk contribs created page 概率论与数理统计 (Spring 2025)/第二次作业提交名单 (Created page with " 如有错漏请邮件联系助教. <center> {| class="wikitable" |- ! 学号 !! 姓名 |- | 231840166 || 赵少凡 |- | 231200035 || 葛翰飞 |- | 231240011 || 陈力琰 |- | 231840058 || 王润希 |- | 231880123 || 陆博文 |- | 231240005 || 王甚易 |- | 231880394 || 翟笑晨 |- | 231240047 || 姜淮仁 |- | 231880152 || 李佳骏 |- | 231240015 || 邱文宣 |- | 231240002 || 余孟凡 |- | 231098046 || 李方泽 |- | 231240060 || 侯佳松 |- | 23124...")
• 01:38, 27 March 2025 Liuexp talk contribs deleted page File:计算方法6-2025.pdf (Deleted old revision 20250327013757!计算方法6-2025.pdf: Duplicated file: content was: "计算方法6-2025", and the only contributor was "Liuexp" (talk))
• 01:37, 27 March 2025 Liuexp talk contribs uploaded a new version of File:计算方法6-2025.pdf
• 09:58, 26 March 2025 Etone talk contribs created page 组合数学 (Fall 2025)/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...")
• 09:56, 26 March 2025 Etone talk contribs created page 组合数学 (Fall 2025)/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...")
• 10:03, 21 March 2025 Etone talk contribs created page 概率论与数理统计 (Spring 2025)/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...")
• 09:58, 21 March 2025 Etone talk contribs created page 组合数学 (Fall 2025)/Pólya's theory of counting (Created page with "== Groups == A group <math>(G,\cdot)</math> is set <math>G</math> along with a binary operator <math>\cdot</math> which satisfies the following axioms: * ''closure'': <math>\forall g,h\in G, g\cdot h \in G</math>; * ''associativity'': <math>\forall f,g,h\in G, f\cdot(g\cdot h)=(f\cdot g)\cdot h</math>; * ''identity'': there exists a special element <math>e\in G</math>, called the '''identity''', such that <math>e\cdot g=g</math> for any <math>g\in G</math>; * ''inverse''...")
• 07:08, 19 March 2025 Houzhe talk contribs created page File:Computational Method 2025 Assignments 3.pdf
• 07:08, 19 March 2025 Houzhe talk contribs uploaded File:Computational Method 2025 Assignments 3.pdf
• 03:12, 19 March 2025 Kvrmnks talk contribs created page 计算方法 Numerical method (Spring 2025)/Homework2 提交名单 (Created page with " 如有错漏请邮件联系助教. <center> {| class="wikitable" |- ! 学号 !! 姓名 |- | 221220090 || 周思桥 |- | 221240002 || 季悦宁 |- | 221240040 || 郑雯琪 |- | 231098068 || 戎昱 |- | 231098091 || 刘棣文 |- | 231098166 || 陈展 |- | 231200035 || 葛翰飞 |- | 231220006 || 陆华均 |- | 231220036 || 周楚函 |- | 231220049 || 张泽宇 |- | 231220065 || 劳汉显 |- | 231220067 || 黄裕书琪 |- | 231220071 || 吴江涛 |- | 23122012...")
• 14:53, 16 March 2025 Gispzjz talk contribs created page 组合数学 (Spring 2025)/Problem Set 1 (Created page with "== Problem 1 == Fix positive integers <math>n</math> and <math>k</math>. Let <math>S</math> be a set with <math>|S|=n</math>. Find the numbers of <math>k</math>-tuples <math>(T_1,T_2,\dots,T_k)</math> of subsets <math>T_i</math> of <math>S</math> subject to each of the following conditions separately. Briefly explain your answer. * <math>T_1\subseteq T_2\subseteq \cdots \subseteq T_k.</math> * The <math> T_i</math>s are pairwise disjoint. * <math> T_1\cup T_2\cup \cdots...")