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class="post-meta-item"><span class="post-meta-item-icon"><i class="fa fa-calendar-check-o"></i></span> <span class="post-meta-item-text">Edited on</span> <time title="Modified: 2023-Jan-01 10:34:13" itemprop="dateModified" datetime="2023-01-01T10:34:13+08:00">2023-Jan-01</time></span></div></header><div class="post-body" itemprop="articleBody"><p>年终了，做一些回忆和整理。</p><div class="post-button"> <a class="btn" href="/blog/posts/2022/#more" rel="contents">Read more &raquo;</a></div></div><footer class="post-footer"><div class="post-eof"></div></footer></article><article itemscope itemtype="http://schema.org/Article" class="post-block" lang="en"><link itemprop="mainEntityOfPage" href="https://schtonn.github.io/blog/posts/t-note/"><span hidden itemprop="author" itemscope itemtype="http://schema.org/Person"><meta itemprop="image" content="/blog/images/avatar.gif"><meta itemprop="name" content="Alex"><meta itemprop="description" content="blog"></span><script type="text/javascript" src="/blog/js/md5.js"></script><script></script><script>document.oncopy=function(e){window.event&&(e=window.event);try{var t=e.srcElement;return"INPUT"==t.tagName&&"text"==t.type.toLowerCase()||"TEXTAREA"==t.tagName}catch(e){return!1}}</script><span hidden itemprop="publisher" itemscope itemtype="http://schema.org/Organization"><meta itemprop="name" content="schtonn"></span><header class="post-header"><h2 class="post-title" itemprop="name headline"> <a href="/blog/posts/t-note/" class="post-title-link" itemprop="url">差劲、无聊记录</a></h2><div class="post-meta"><span class="post-meta-item"><span class="post-meta-item-icon"><i class="fa fa-calendar-o"></i></span> <span class="post-meta-item-text">Posted on</span> <time title="Created: 2022-Oct-15 13:40:48" itemprop="dateCreated datePublished" datetime="2022-10-15T13:40:48+08:00">2022-Oct-15</time></span><span class="post-meta-item"><span class="post-meta-item-icon"><i class="fa fa-calendar-check-o"></i></span> <span class="post-meta-item-text">Edited on</span> <time title="Modified: 2023-Feb-17 19:39:04" itemprop="dateModified" datetime="2023-02-17T19:39:04+08:00">2023-Feb-17</time></span></div></header><div class="post-body" itemprop="articleBody"><link rel="stylesheet" href="/blog/css/spoiler.css" type="text/css"><script src="/blog/js/spoiler.js" type="text/javascript" async></script><h2 id="section">2022.10.14</h2><ul><li>第一次化学统测，最后一题需要同时考虑正负电荷、物质的量而确定答案，考场上没做出来，感极而悲，认识到现在的题目已不是直接考虑就能完成，遂开始了差劲、无聊事项的记录。<ul><li>化学大题考虑事项：计算物质的量、正负电荷、<a href="/blog/posts/dissolve">是否可溶</a>、是否为弱电解质，注意弱电解质也在离子方程式里。</li></ul></li><li>数学：<ul><li>对 <span class="math inline">\(f(x)=(ax-1)(x+2)\)</span> 正负性分类，讨论半天只在 <span class="math inline">\(a=\dfrac{1}{2}\)</span> 点分类，忘了在零点分，痛失三分。</li><li>要学会在草稿作图，有助于思路。</li></ul></li><li>物理：匀加速直线运动求距离忘除二，导致两问全错。</li><li>英语：定语从句填空不能空着。</li></ul><div class="post-button"> <a class="btn" href="/blog/posts/t-note/#more" rel="contents">Read more &raquo;</a></div></div><footer class="post-footer"><div class="post-eof"></div></footer></article><article itemscope itemtype="http://schema.org/Article" class="post-block" lang="en"><link itemprop="mainEntityOfPage" href="https://schtonn.github.io/blog/posts/note/"><span hidden itemprop="author" itemscope itemtype="http://schema.org/Person"><meta itemprop="image" content="/blog/images/avatar.gif"><meta itemprop="name" content="Alex"><meta itemprop="description" content="blog"></span><script type="text/javascript" src="/blog/js/md5.js"></script><script></script><script>document.oncopy=function(e){window.event&&(e=window.event);try{var t=e.srcElement;return"INPUT"==t.tagName&&"text"==t.type.toLowerCase()||"TEXTAREA"==t.tagName}catch(e){return!1}}</script><span hidden itemprop="publisher" itemscope itemtype="http://schema.org/Organization"><meta itemprop="name" content="schtonn"></span><header class="post-header"><h2 class="post-title" itemprop="name headline"> <a href="/blog/posts/note/" class="post-title-link" itemprop="url">一些记录</a></h2><div class="post-meta"><span class="post-meta-item"><span class="post-meta-item-icon"><i class="fa fa-calendar-o"></i></span> <span class="post-meta-item-text">Posted on</span> <time title="Created: 2022-Sep-18 11:28:26" itemprop="dateCreated datePublished" datetime="2022-09-18T11:28:26+08:00">2022-Sep-18</time></span><span class="post-meta-item"><span class="post-meta-item-icon"><i class="fa fa-calendar-check-o"></i></span> <span class="post-meta-item-text">Edited on</span> <time title="Modified: 2022-Oct-19 23:31:57" itemprop="dateModified" datetime="2022-10-19T23:31:57+08:00">2022-Oct-19</time></span></div></header><div class="post-body" itemprop="articleBody"><h2 id="section">2022.9.17</h2><h3 id="组合数技巧">组合数技巧</h3><p>对于 <span class="math inline">\(\bmod 2\)</span> 的组合数，进行卢卡斯后可得出结论： <span class="math inline">\(C_n^m=[n\textsf{&amp;}m=m]\)</span></p><h2 id="section-1">2022.9.24</h2><h3 id="可后悔贪心">可后悔贪心</h3><blockquote><p>A 城市有一个巨大的圆形广场，为了绿化环境和净化空气，市政府决定沿圆形广场外圈种一圈树。园林部门得到指令后，初步规划出 <span class="math inline">\(n\)</span> 个种树的位置，顺时针编号 <span class="math inline">\(1\)</span> 到 <span class="math inline">\(n\)</span>。并且每个位置都有一个美观度 <span class="math inline">\(A_i\)</span>，如果在这里种树就可以得到这Ai的美观度。但由于A城市土壤肥力欠佳，两棵树决不能种在相邻的位置（<span class="math inline">\(i\)</span> 号位置和 <span class="math inline">\(i+1\)</span> 号位置叫相邻位置。值得注意的是 <span class="math inline">\(1\)</span> 号和 <span class="math inline">\(n\)</span> 号也算相邻位置！）。</p><p>最终市政府给园林部门提供了 <span class="math inline">\(m\)</span> 棵树苗并要求全部种上，请你帮忙设计种树方案使得美观度总和最大。如果无法将 <span class="math inline">\(m\)</span> 棵树苗全部种上，给出无解信息。</p></blockquote><div class="post-button"> <a class="btn" href="/blog/posts/note/#more" rel="contents">Read more &raquo;</a></div></div><footer class="post-footer"><div class="post-eof"></div></footer></article><article itemscope itemtype="http://schema.org/Article" class="post-block" lang="en"><link itemprop="mainEntityOfPage" href="https://schtonn.github.io/blog/posts/tarjan/"><span hidden itemprop="author" itemscope itemtype="http://schema.org/Person"><meta itemprop="image" content="/blog/images/avatar.gif"><meta itemprop="name" content="Alex"><meta itemprop="description" content="blog"></span><script type="text/javascript" src="/blog/js/md5.js"></script><script></script><script>document.oncopy=function(e){window.event&&(e=window.event);try{var t=e.srcElement;return"INPUT"==t.tagName&&"text"==t.type.toLowerCase()||"TEXTAREA"==t.tagName}catch(e){return!1}}</script><span hidden itemprop="publisher" itemscope itemtype="http://schema.org/Organization"><meta itemprop="name" content="schtonn"></span><header class="post-header"><h2 class="post-title" itemprop="name headline"> <a href="/blog/posts/tarjan/" class="post-title-link" itemprop="url">Tarjan 算法</a></h2><div class="post-meta"><span class="post-meta-item"><span class="post-meta-item-icon"><i class="fa fa-calendar-o"></i></span> <span class="post-meta-item-text">Posted on</span> <time title="Created: 2022-Jul-10 17:12:17" itemprop="dateCreated datePublished" datetime="2022-07-10T17:12:17+08:00">2022-Jul-10</time></span><span class="post-meta-item"><span class="post-meta-item-icon"><i class="fa fa-calendar-check-o"></i></span> <span class="post-meta-item-text">Edited on</span> <time title="Modified: 2022-Oct-19 23:32:24" itemprop="dateModified" datetime="2022-10-19T23:32:24+08:00">2022-Oct-19</time></span></div></header><div class="post-body" itemprop="articleBody"><h2 id="前置知识">前置知识</h2><p>基本图论，dfs 序和搜索树，栈</p><h2 id="引入">引入</h2><p>Tarjan 算法由 Robert Tarjan 提出，具有线性复杂度，是图论中非常实用且通用的一个算法。</p><p>针对无向图，可以用来求图中的<strong>桥</strong><em>（删去后两边变得不连通的边，也叫割边）</em>、<strong>割点</strong><em>（删去后它连接的部分变得不连通的点）</em>；</p><p>针对有向图还可以进行缩点，也就是把所有<strong>能互相连通的点</strong><em>（这个叫强连通分量）</em> 缩成一个点，在让图变无环的同时保留了一些性质，便于计算。</p><div class="post-button"> <a class="btn" href="/blog/posts/tarjan/#more" rel="contents">Read more &raquo;</a></div></div><footer class="post-footer"><div class="post-eof"></div></footer></article><article itemscope itemtype="http://schema.org/Article" class="post-block" lang="en"><link itemprop="mainEntityOfPage" href="https://schtonn.github.io/blog/posts/dissolve/"><span hidden itemprop="author" itemscope itemtype="http://schema.org/Person"><meta itemprop="image" content="/blog/images/avatar.gif"><meta itemprop="name" content="Alex"><meta itemprop="description" content="blog"></span><script type="text/javascript" src="/blog/js/md5.js"></script><script></script><script>document.oncopy=function(e){window.event&&(e=window.event);try{var t=e.srcElement;return"INPUT"==t.tagName&&"text"==t.type.toLowerCase()||"TEXTAREA"==t.tagName}catch(e){return!1}}</script><span hidden itemprop="publisher" itemscope itemtype="http://schema.org/Organization"><meta itemprop="name" content="schtonn"></span><header class="post-header"><h2 class="post-title" itemprop="name headline"> <a href="/blog/posts/dissolve/" class="post-title-link" itemprop="url">各种盐的溶解度整理</a></h2><div class="post-meta"><span class="post-meta-item"><span class="post-meta-item-icon"><i class="fa fa-calendar-o"></i></span> <span class="post-meta-item-text">Posted on</span> <time title="Created: 2022-Feb-19 11:58:33" itemprop="dateCreated datePublished" datetime="2022-02-19T11:58:33+08:00">2022-Feb-19</time></span><span class="post-meta-item"><span class="post-meta-item-icon"><i class="fa fa-calendar-check-o"></i></span> <span class="post-meta-item-text">Edited on</span> <time title="Modified: 2022-Oct-17 22:13:07" itemprop="dateModified" datetime="2022-10-17T22:13:07+08:00">2022-Oct-17</time></span></div></header><div class="post-body" itemprop="articleBody"><table><thead><tr class="header"><th>-</th><th style="text-align:center"><span class="math inline">\(\text{SO}_4^{2-}\)</span></th><th style="text-align:center"><span class="math inline">\(\text{CO}_3^{2-}\)</span></th><th style="text-align:center"><span class="math inline">\(\text{NO}_3^-\)</span></th><th style="text-align:center"><span class="math inline">\(\text{OH}^-\)</span></th><th style="text-align:center"><span class="math inline">\(\text{Cl}^-\)</span></th></tr></thead><tbody><tr class="odd"><td><span class="math inline">\(\text{Ba}^{2+}\)</span></td><td style="text-align:center">不</td><td style="text-align:center">难</td><td style="text-align:center">可</td><td style="text-align:center">可</td><td style="text-align:center">可</td></tr><tr class="even"><td><span class="math inline">\(\text{Cu}^{2+}\)</span></td><td style="text-align:center">可</td><td style="text-align:center">-</td><td style="text-align:center">可</td><td style="text-align:center">不</td><td style="text-align:center">可</td></tr><tr class="odd"><td><span class="math inline">\(\text{K}^{+}\)</span></td><td style="text-align:center">可</td><td style="text-align:center">可</td><td style="text-align:center">可</td><td style="text-align:center">可</td><td style="text-align:center">可</td></tr><tr class="even"><td><span class="math inline">\(\text{Al}^{3+}\)</span></td><td style="text-align:center">可</td><td style="text-align:center">-</td><td style="text-align:center">可</td><td style="text-align:center">不</td><td style="text-align:center">可</td></tr><tr class="odd"><td><span class="math inline">\(\text{Mg}^{2+}\)</span></td><td style="text-align:center">可</td><td style="text-align:center">难</td><td style="text-align:center">可</td><td style="text-align:center">难</td><td style="text-align:center">可</td></tr><tr class="even"><td><span class="math inline">\(\text{Ca}^{2+}\)</span></td><td style="text-align:center">微</td><td style="text-align:center">不</td><td style="text-align:center">可</td><td style="text-align:center">难</td><td style="text-align:center">可</td></tr><tr class="odd"><td><span class="math inline">\(\text{Fe}^{2+}\)</span></td><td style="text-align:center">可</td><td style="text-align:center">不</td><td style="text-align:center">可</td><td style="text-align:center">不</td><td style="text-align:center">可</td></tr><tr class="even"><td><span class="math inline">\(\text{Zn}^{2+}\)</span></td><td style="text-align:center">可</td><td style="text-align:center">不</td><td style="text-align:center">可</td><td style="text-align:center">不</td><td style="text-align:center">可</td></tr><tr class="odd"><td><span class="math inline">\(\text{Mn}^{2+}\)</span></td><td style="text-align:center">可</td><td style="text-align:center">不</td><td style="text-align:center">可</td><td style="text-align:center">难</td><td style="text-align:center">可</td></tr><tr class="even"><td><span class="math inline">\(\text{Na}^+\)</span></td><td style="text-align:center">可</td><td style="text-align:center">可</td><td style="text-align:center">可</td><td style="text-align:center">可</td><td style="text-align:center">可</td></tr><tr class="odd"><td><span class="math inline">\(\text{Ag}^+\)</span></td><td style="text-align:center">不</td><td style="text-align:center">难</td><td style="text-align:center">可</td><td style="text-align:center">-</td><td style="text-align:center">可</td></tr></tbody></table></div><footer class="post-footer"><div class="post-eof"></div></footer></article><article itemscope itemtype="http://schema.org/Article" class="post-block" lang="en"><link itemprop="mainEntityOfPage" href="https://schtonn.github.io/blog/posts/zhengzhi-8xia/"><span hidden itemprop="author" itemscope itemtype="http://schema.org/Person"><meta itemprop="image" content="/blog/images/avatar.gif"><meta itemprop="name" content="Alex"><meta itemprop="description" content="blog"></span><script type="text/javascript" src="/blog/js/md5.js"></script><script></script><script>document.oncopy=function(e){window.event&&(e=window.event);try{var t=e.srcElement;return"INPUT"==t.tagName&&"text"==t.type.toLowerCase()||"TEXTAREA"==t.tagName}catch(e){return!1}}</script><span hidden itemprop="publisher" itemscope itemtype="http://schema.org/Organization"><meta itemprop="name" content="schtonn"></span><header class="post-header"><h2 class="post-title" itemprop="name headline"> <a href="/blog/posts/zhengzhi-8xia/" class="post-title-link" itemprop="url">八下政治总结</a></h2><div class="post-meta"><span class="post-meta-item"><span class="post-meta-item-icon"><i class="fa fa-calendar-o"></i></span> <span class="post-meta-item-text">Posted on</span> <time title="Created: 2022-Feb-17 11:36:30 / Modified: 23:15:20" itemprop="dateCreated datePublished" datetime="2022-02-17T11:36:30+08:00">2022-Feb-17</time></span></div></header><div class="post-body" itemprop="articleBody"><h1 id="第一单元-坚持宪法至上">第一单元 坚持宪法至上</h1><h2 id="第一课-维护宪法权威">第一课 维护宪法权威</h2><h3 id="公民权利的保障书">公民权利的保障书</h3><ol type="1"><li>国家权力属于人民<ul><li>中国是工人阶级领导的、以工农联盟为基础的人民民主专政的社会主义国家；（宪法第一条）</li><li>国家的一切权力属于人民，是我国宪法的基本原则；（第二条）</li><li>宪法规定社会主义经济制度，是~的经济基础；</li><li>宪法规定社会主义政治制度，是~的基本途径和形式；</li><li>宪法规定广泛的公民基本权利，保障措施；</li><li>宪法规定武装力量属于人民。<div class="post-button"> <a class="btn" href="/blog/posts/zhengzhi-8xia/#more" rel="contents">Read more &raquo;</a></div></li></ul></li></ol></div><footer class="post-footer"><div class="post-eof"></div></footer></article><article itemscope itemtype="http://schema.org/Article" class="post-block" lang="en"><link itemprop="mainEntityOfPage" href="https://schtonn.github.io/blog/posts/emperor/"><span hidden itemprop="author" itemscope itemtype="http://schema.org/Person"><meta itemprop="image" content="/blog/images/avatar.gif"><meta itemprop="name" content="Alex"><meta itemprop="description" content="blog"></span><script type="text/javascript" src="/blog/js/md5.js"></script><script></script><script>document.oncopy=function(e){window.event&&(e=window.event);try{var t=e.srcElement;return"INPUT"==t.tagName&&"text"==t.type.toLowerCase()||"TEXTAREA"==t.tagName}catch(e){return!1}}</script><span hidden itemprop="publisher" itemscope itemtype="http://schema.org/Organization"><meta itemprop="name" content="schtonn"></span><header class="post-header"><h2 class="post-title" itemprop="name headline"> <a href="/blog/posts/emperor/" class="post-title-link" itemprop="url">中国历史皇帝整理</a></h2><div class="post-meta"><span class="post-meta-item"><span class="post-meta-item-icon"><i class="fa fa-calendar-o"></i></span> <span class="post-meta-item-text">Posted on</span> <time title="Created: 2022-Feb-06 17:56:27 / Modified: 18:08:50" itemprop="dateCreated datePublished" datetime="2022-02-06T17:56:27+08:00">2022-Feb-06</time></span></div></header><div class="post-body" itemprop="articleBody"><h2 id="秦朝">秦朝</h2><p>（统一后，公元前221~201，共15年，历三帝，赢姓） 1. 秦始皇（赢政）——中国的第一个皇帝，12年 2. 秦二世（胡亥），后被赵高所杀，3年 3. 子缨，斩杀赵高，1年</p><h2 id="汉朝">汉朝</h2><h3 id="西汉">西汉</h3><p>（公元前206~公元8年，共214年，刘姓，历 1. 汉高祖（刘邦）——大汉开国皇帝，12年 2. 汉惠帝（刘盈）——来去匆匆，过眼云烟 3. 少帝（吕后专政），8年 4. 汉文帝（刘恒），23年 5. 汉景帝（刘启），政绩并不代表其成功，16年 6. 汉武帝（刘彻）——开天辟地，建元，54年</p><div class="post-button"> <a class="btn" href="/blog/posts/emperor/#more" rel="contents">Read more &raquo;</a></div></div><footer class="post-footer"><div class="post-eof"></div></footer></article><article itemscope itemtype="http://schema.org/Article" class="post-block" lang="en"><link itemprop="mainEntityOfPage" href="https://schtonn.github.io/blog/posts/katyusha/"><span hidden itemprop="author" itemscope itemtype="http://schema.org/Person"><meta itemprop="image" content="/blog/images/avatar.gif"><meta itemprop="name" content="Alex"><meta itemprop="description" content="blog"></span><script type="text/javascript" src="/blog/js/md5.js"></script><script></script><script>document.oncopy=function(e){window.event&&(e=window.event);try{var t=e.srcElement;return"INPUT"==t.tagName&&"text"==t.type.toLowerCase()||"TEXTAREA"==t.tagName}catch(e){return!1}}</script><span hidden itemprop="publisher" itemscope itemtype="http://schema.org/Organization"><meta itemprop="name" content="schtonn"></span><header class="post-header"><h2 class="post-title" itemprop="name headline"> <a href="/blog/posts/katyusha/" class="post-title-link" itemprop="url">用管乐还原《喀秋莎》</a></h2><div class="post-meta"><span class="post-meta-item"><span class="post-meta-item-icon"><i class="fa fa-calendar-o"></i></span> <span class="post-meta-item-text">Posted on</span> <time title="Created: 2022-Jan-23 11:38:55 / Modified: 11:44:50" itemprop="dateCreated datePublished" datetime="2022-01-23T11:38:55+08:00">2022-Jan-23</time></span></div></header><div class="post-body" itemprop="articleBody"><center><audio src="/blog/data/katyusha.mp3" controls></audio></center></div><footer class="post-footer"><div class="post-eof"></div></footer></article><article itemscope itemtype="http://schema.org/Article" class="post-block" lang="en"><link itemprop="mainEntityOfPage" href="https://schtonn.github.io/blog/posts/powersum/"><span hidden itemprop="author" itemscope itemtype="http://schema.org/Person"><meta itemprop="image" content="/blog/images/avatar.gif"><meta itemprop="name" content="Alex"><meta itemprop="description" content="blog"></span><script type="text/javascript" src="/blog/js/md5.js"></script><script></script><script>document.oncopy=function(e){window.event&&(e=window.event);try{var t=e.srcElement;return"INPUT"==t.tagName&&"text"==t.type.toLowerCase()||"TEXTAREA"==t.tagName}catch(e){return!1}}</script><span hidden itemprop="publisher" itemscope itemtype="http://schema.org/Organization"><meta itemprop="name" content="schtonn"></span><header class="post-header"><h2 class="post-title" itemprop="name headline"> <a href="/blog/posts/powersum/" class="post-title-link" itemprop="url">自然数幂求和公式</a></h2><div class="post-meta"><span class="post-meta-item"><span class="post-meta-item-icon"><i class="fa fa-calendar-o"></i></span> <span class="post-meta-item-text">Posted on</span> <time title="Created: 2021-Dec-12 12:24:01" itemprop="dateCreated datePublished" datetime="2021-12-12T12:24:01+08:00">2021-Dec-12</time></span><span class="post-meta-item"><span class="post-meta-item-icon"><i class="fa fa-calendar-check-o"></i></span> <span class="post-meta-item-text">Edited on</span> <time title="Modified: 2022-Oct-19 23:10:22" itemprop="dateModified" datetime="2022-10-19T23:10:22+08:00">2022-Oct-19</time></span></div></header><div class="post-body" itemprop="articleBody"><p>（<span class="math inline">\(\text{C}^m_n\)</span> 代表从 <span class="math inline">\(n\)</span> 个不同物品里面选 <span class="math inline">\(m\)</span> 个，有多少种选法）</p><p>（<span class="math inline">\(\sum\limits_{i=0}^n\text{f}(i)\)</span> 表示从 <span class="math inline">\(0\)</span> 到 <span class="math inline">\(n\)</span> 对 <span class="math inline">\(\text{f}(i)\)</span> 求和）</p><p>（约定 <span class="math inline">\(\text{C}^0_n=1\)</span>）</p><blockquote><p>引理：n 次方差公式 <span class="math display">\[(m+1)^{k+1}-m^{k+1}=\sum_{i=0}^{k}\text{C}^i_{k+1}m^i\]</span></p></blockquote><p>证：</p><p><span class="math display">\[\sum^n_{m=1}(m+1)^{k+1}-m^{k+1}=(n+1)^{k+1}-1^{k+1}\]</span> <span class="math display">\[=\sum_{i=0}^k\text{C}^i_{k+1}\left(\sum^n_{m=1}m^i\right)\]</span> <span class="math display">\[=\text{C}^k_{k+1}\left(\sum^n_{m=1}m^k\right)+\sum^{k-1}_{i=0}\text{C}^i_{k+1}\left(\sum^n_{m=1}m^i\right)\]</span></p><p>因此有 <span class="math display">\[\sum^n_{m=1}m^k=\dfrac{1}{\text{C}^k_{k+1}}\left[(n+1)^{k+1}-1-\sum^{k-1}_{i=0}\text{C}^i_{k+1}\left(\sum^n_{m=1}m^i\right)\right]\]</span></p></div><footer class="post-footer"><div class="post-eof"></div></footer></article><article itemscope itemtype="http://schema.org/Article" class="post-block" lang="en"><link itemprop="mainEntityOfPage" href="https://schtonn.github.io/blog/posts/group/"><span hidden itemprop="author" itemscope itemtype="http://schema.org/Person"><meta itemprop="image" content="/blog/images/avatar.gif"><meta itemprop="name" content="Alex"><meta itemprop="description" content="blog"></span><script type="text/javascript" src="/blog/js/md5.js"></script><script></script><script>document.oncopy=function(e){window.event&&(e=window.event);try{var t=e.srcElement;return"INPUT"==t.tagName&&"text"==t.type.toLowerCase()||"TEXTAREA"==t.tagName}catch(e){return!1}}</script><span hidden itemprop="publisher" itemscope itemtype="http://schema.org/Organization"><meta itemprop="name" content="schtonn"></span><header class="post-header"><h2 class="post-title" itemprop="name headline"> <a href="/blog/posts/group/" class="post-title-link" itemprop="url">关于群论的一些东西</a></h2><div class="post-meta"><span class="post-meta-item"><span class="post-meta-item-icon"><i class="fa fa-calendar-o"></i></span> <span class="post-meta-item-text">Posted on</span> <time title="Created: 2021-May-31 19:51:15" itemprop="dateCreated datePublished" datetime="2021-05-31T19:51:15+08:00">2021-May-31</time></span><span class="post-meta-item"><span class="post-meta-item-icon"><i class="fa fa-calendar-check-o"></i></span> <span class="post-meta-item-text">Edited on</span> <time title="Modified: 2022-Oct-19 23:33:01" itemprop="dateModified" datetime="2022-10-19T23:33:01+08:00">2022-Oct-19</time></span></div></header><div class="post-body" itemprop="articleBody"><h2 id="定义">定义</h2><p>定义 <span class="math inline">\((S,\cdot)\)</span> 为一个群，其中 <span class="math inline">\(S\)</span> 是一个非空集合，<span class="math inline">\(\cdot\)</span> 是一个二元运算。</p><p>则它满足以下四个条件：</p><ol type="1"><li>封闭性：<span class="math inline">\(\forall a,b\in S, a\cdot b\in S,\)</span></li><li>结合律：<span class="math inline">\(\forall a,b,c\in S,(a\cdot b)\cdot c=a\cdot(b\cdot c)\)</span></li><li>单位元：<span class="math inline">\(\exists e\in S,\forall a \in S, a\cdot e=e\cdot a=a\)</span></li><li>逆元：<span class="math inline">\(\forall a\in S,\exists a^{-1}\in S, \text{s.t.}a\cdot a^{-1}=a^{-1}\cdot a=e\)</span></li></ol><div class="post-button"> <a class="btn" href="/blog/posts/group/#more" rel="contents">Read more &raquo;</a></div></div><footer class="post-footer"><div class="post-eof"></div></footer></article><nav class="pagination"> <span class="page-number current">1</span><a class="page-number" href="/blog/page/2/">2</a><span class="space">&hellip;</span><a class="page-number" href="/blog/page/4/">4</a><a class="extend next" rel="next" href="/blog/page/2/"><i class="fa fa-angle-right" aria-label="Next page"></i></a></nav></div><script>
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