[原创]N阶正方体色子阵魔方基本置换分析和证明:第一版
<p><strong>一。相似变换</strong></p><p><strong>定义</strong></p><p>设有公式F和f，f'是f的逆，F'=f'+F+f,则将F不变的所有F'互称关于F的相似变换，简称相似变换<br/><br/></p><p><strong>状态</strong></p><p>设S0代表复原状态，F与F'是相似变换，变换F(S0)=S1，变换F'(S0)=S2，从簇层面：</p><p>1.S1与S2参与变换的块的数量相同</p><p>2.S1与S2参与变换的块可能全部相同或部分相同或互不相同，差异由f决定，其它一切状态方面的特征S1与S2完全相同。</p><p><strong>推论</strong></p><p>1.互为相似变换的公式有相同的公式循环周期.但公式循环周期相同的公式不一定是相似变换</p><p>2.如果F变换前的状态与变换后的状态相同，则F'变换前的状态与变换后的状态相同</p><p><strong>说明</strong></p><p>f输送块，F变换块，f'让没有参与F变换的块复位。相似变换的重要意义在于使得变换与块的位置没有必然关联。相似变换定义的简洁性与其解释魔方变换的广义性，使之成为构建魔方基本变换定律最重要的基石</p><p></p><p><strong>举例</strong></p><p>例1：如果簇存在一个四轮换，则簇的任意四个块可四轮换</p><p>例2：如果簇存在一个三置换，则簇的任意三个块可以三置换</p><p>例3：如果簇的二个块可以独立变换色向，则簇的任意二个块可以独立变换色向</p><p><strong>强调</strong></p><p>相似变换是以下几个主题讨论的基础</p>[此贴子已经被作者于2007-4-10 0:03:59编辑过]
<p><strong>二。3置换证明</strong></p><p><table cellspacing="0" cellpadding="0" width="432" border="0" xstr="" style="WIDTH: 324pt; BORDER-COLLAPSE: collapse;"><colgroup><col span="6" width="72" style="WIDTH: 54pt;"></col></colgroup><tbody><tr height="19" style="HEIGHT: 14.25pt;"><td class="xl24" width="72" height="19" style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext 0.5pt solid; BORDER-LEFT: windowtext 0.5pt solid; WIDTH: 54pt; BORDER-BOTTOM: windowtext 0.5pt solid; HEIGHT: 14.25pt; BACKGROUND-COLOR: transparent;"><font face="宋体">A</font></td><td class="xl24" align="right" width="72" xnum="" style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext 0.5pt solid; BORDER-LEFT: windowtext; WIDTH: 54pt; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent;"><font face="宋体">1</font></td><td class="xl24" align="right" width="72" xnum="" style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext 0.5pt solid; BORDER-LEFT: windowtext; WIDTH: 54pt; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent;"><font face="宋体">2</font></td><td class="xl24" align="right" width="72" xnum="" style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext 0.5pt solid; BORDER-LEFT: windowtext; WIDTH: 54pt; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent;"><font face="宋体">3</font></td><td class="xl24" align="right" width="72" xnum="" style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext 0.5pt solid; BORDER-LEFT: windowtext; WIDTH: 54pt; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent;"><font face="宋体">4</font></td><td class="xl24" align="right" width="72" xnum="" style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext 0.5pt solid; BORDER-LEFT: windowtext; WIDTH: 54pt; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent;"><font face="宋体">5</font></td></tr><tr height="19" style="HEIGHT: 14.25pt;"><td class="xl24" height="19" style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext 0.5pt solid; BORDER-BOTTOM: windowtext 0.5pt solid; HEIGHT: 14.25pt; BACKGROUND-COLOR: transparent;"><font face="宋体">B</font></td><td class="xl24" align="right" xnum="" style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent;"><font face="宋体">4</font></td><td class="xl24" align="right" xnum="" style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent;"><font face="宋体">1</font></td><td class="xl24" align="right" xnum="" style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent;"><font face="宋体">2</font></td><td class="xl24" align="right" xnum="" style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent;"><font face="宋体">3</font></td><td class="xl24" align="right" xnum="" style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent;"><font face="宋体">5</font></td></tr><tr height="19" style="HEIGHT: 14.25pt;"><td class="xl24" height="19" style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext 0.5pt solid; BORDER-BOTTOM: windowtext 0.5pt solid; HEIGHT: 14.25pt; BACKGROUND-COLOR: transparent;"><font face="宋体">C</font></td><td class="xl24" align="right" xnum="" style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent;"><font face="宋体">4</font></td><td class="xl24" align="right" xnum="" style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent;"><font face="宋体">2</font></td><td class="xl24" align="right" xnum="" style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent;"><font face="宋体">3</font></td><td class="xl24" align="right" xnum="" style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent;"><font face="宋体">5</font></td><td class="xl24" align="right" xnum="" style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent;"><font face="宋体">1</font></td></tr><tr height="19" style="HEIGHT: 14.25pt;"><td class="xl24" height="19" style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext 0.5pt solid; BORDER-BOTTOM: windowtext 0.5pt solid; HEIGHT: 14.25pt; BACKGROUND-COLOR: transparent;"><font face="宋体"> </font></td><td class="xl24" style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent;"><font face="宋体"> </font></td><td class="xl24" style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent;"><font face="宋体"> </font></td><td class="xl24" style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent;"><font face="宋体"> </font></td><td class="xl24" style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent;"><font face="宋体"> </font></td><td class="xl24" style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent;"><font face="宋体"> </font></td></tr><tr height="19" style="HEIGHT: 14.25pt;"><td class="xl24" height="19" style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext 0.5pt solid; BORDER-BOTTOM: windowtext 0.5pt solid; HEIGHT: 14.25pt; BACKGROUND-COLOR: transparent;"><font face="宋体"> </font></td><td class="xl24" align="right" xnum="" style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent;"><font face="宋体">4</font></td><td class="xl24" style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent;"><font face="宋体"> </font></td><td class="xl24" style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent;"><font face="宋体"> </font></td><td class="xl24" align="right" xnum="" style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent;"><font face="宋体">5</font></td><td class="xl24" align="right" xnum="" style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent;"><font face="宋体">1</font></td></tr></tbody></table></p><p>1.四轮换是魔方结构决定的公理</p><p>2.A行代表块的初始位置</p><p>3.B行代表对A行的1，2，3，4块进行次向右的四轮换,生成环C(4,1,2,3)</p><p>4.C行代表对B行的块5，3，2，1块进行一次向左的四轮换,生成环C(4，5，1)，即所谓的三置换</p><p>5.依据相似变换原理,只要有一种三置换成立，那么任意三个块可以进行三置换</p><p><strong>说明</strong></p><p>四轮换是魔方结构定义的最基本的置换，正是依据相似变换原理，才使得列表讨论置换而不管魔方块的具体位置才成为可能，即所谓的置换变换与位置无关。</p>
[此贴子已经被作者于2007-3-18 9:35:02编辑过]
<p><strong>三.证明3置换可以将单偶环分解为二置换<br/></strong></p><p> A 1, 2, 3, 4 … n-3, n-2, n-1, n<br/> B n, 1, 2, 3, 4 … n-3, n-2, n-1<br/> C 1, 2, n, 3, 4 … n-3, n-2, n-1<br/> D 3, 4 ,n … n-3, n-2, n-1<br/> … <br/> n/2 n-5,n-4, n ,n-3, n-2, n-1<br/> (n/2)-1 n-3, n-2, n ,n-1</p><p>1。A行表示块的初始位置，n是一偶数，A行有偶数个块n</p><p>2。B行表示包括所有块的一个偶环</p><p>3。每次取环最左边相邻的三个块向左三置换</p><p>4。C行代表B行的偶环做一次三置换，生成偶环C（n,3,4,...,n-3,n-2,n-1)</p><p>5。D行代表C行的偶环做一次三置换，生成偶环C（n,...,n-3,n-2,n-1)</p><p>6。(n/2)-1行代表n/2行的偶环做一次三置换，生成偶环C（n,n-1)，下面的证明可知三置换无法分解C（n,n-1)</p><p><strong>说明</strong></p><p>同理，可以证明三置换可以完全分解所有奇环。</p>
[此贴子已经被作者于2007-3-18 21:17:24编辑过]
<p><strong>四。证明偶数个偶环可以被三置换完全分解</strong></p><p><table cellspacing="0" cellpadding="0" width="576" border="0" xstr="" style="WIDTH: 432pt; BORDER-COLLAPSE: collapse;"><tbody><tr height="19" style="HEIGHT: 14.25pt;"><td class="xl24" width="72" height="19" style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext 0.5pt solid; BORDER-LEFT: windowtext 0.5pt solid; WIDTH: 54pt; BORDER-BOTTOM: windowtext 0.5pt solid; HEIGHT: 14.25pt; BACKGROUND-COLOR: transparent;"></td><td class="xl24" align="right" width="72" xnum="" style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext 0.5pt solid; BORDER-LEFT-COLOR: windowtext; WIDTH: 54pt; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent;"><font face="宋体">1</font></td><td class="xl24" align="right" width="72" xnum="" style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext 0.5pt solid; BORDER-LEFT-COLOR: windowtext; WIDTH: 54pt; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent;"><font face="宋体">2</font></td><td class="xl24" align="right" width="72" xnum="" style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext 0.5pt solid; BORDER-LEFT-COLOR: windowtext; WIDTH: 54pt; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent;"><font face="宋体">3</font></td><td class="xl24" align="right" width="72" xnum="" style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext 0.5pt solid; BORDER-LEFT-COLOR: windowtext; WIDTH: 54pt; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent;"><font face="宋体">4</font></td><td class="xl24" align="right" width="72" xnum="" style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext 0.5pt solid; BORDER-LEFT-COLOR: windowtext; WIDTH: 54pt; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent;"><font face="宋体">5</font></td><td class="xl24" align="right" width="72" xnum="" style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext 0.5pt solid; BORDER-LEFT-COLOR: windowtext; WIDTH: 54pt; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent;"><font face="宋体">6</font></td><td class="xl24" align="right" width="72" xnum="" style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext 0.5pt solid; BORDER-LEFT-COLOR: windowtext; WIDTH: 54pt; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent;"><font face="宋体">7</font></td></tr><tr height="19" style="HEIGHT: 14.25pt;"><td class="xl24" height="19" style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-LEFT: windowtext 0.5pt solid; BORDER-TOP-COLOR: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; HEIGHT: 14.25pt; BACKGROUND-COLOR: transparent;"><font face="宋体">B</font></td><td class="xl24" align="right" xnum="" style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-LEFT-COLOR: windowtext; BORDER-TOP-COLOR: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent;"><font face="宋体">2</font></td><td class="xl24" align="right" xnum="" style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-LEFT-COLOR: windowtext; BORDER-TOP-COLOR: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent;"><font face="宋体">1</font></td><td class="xl24" align="right" xnum="" style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-LEFT-COLOR: windowtext; BORDER-TOP-COLOR: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent;"><font face="宋体">4</font></td><td class="xl24" align="right" xnum="" style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-LEFT-COLOR: windowtext; BORDER-TOP-COLOR: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent;"><font face="宋体">3</font></td><td class="xl24" align="right" xnum="" style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-LEFT-COLOR: windowtext; BORDER-TOP-COLOR: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent;"><font face="宋体">6</font></td><td class="xl24" align="right" xnum="" style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-LEFT-COLOR: windowtext; BORDER-TOP-COLOR: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent;"><font face="宋体">5</font></td><td class="xl24" align="right" xnum="" style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-LEFT-COLOR: windowtext; BORDER-TOP-COLOR: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent;"><font face="宋体">7</font></td></tr><tr height="19" style="HEIGHT: 14.25pt;"><td class="xl24" height="19" style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-LEFT: windowtext 0.5pt solid; BORDER-TOP-COLOR: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; HEIGHT: 14.25pt; BACKGROUND-COLOR: transparent;"><font face="宋体">C</font></td><td class="xl24" align="right" xnum="" style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-LEFT-COLOR: windowtext; BORDER-TOP-COLOR: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent;"><font face="宋体">4</font></td><td class="xl24" align="right" xnum="" style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-LEFT-COLOR: windowtext; BORDER-TOP-COLOR: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent;"><font face="宋体">2</font></td><td class="xl24" align="right" xnum="" style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-LEFT-COLOR: windowtext; BORDER-TOP-COLOR: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent;"><font face="宋体">1</font></td><td class="xl24" align="right" xnum="" style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-LEFT-COLOR: windowtext; BORDER-TOP-COLOR: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent;"><font face="宋体">3</font></td><td class="xl24" align="right" xnum="" style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-LEFT-COLOR: windowtext; BORDER-TOP-COLOR: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent;"><font face="宋体">6</font></td><td class="xl24" align="right" xnum="" style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-LEFT-COLOR: windowtext; BORDER-TOP-COLOR: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent;"><font face="宋体">5</font></td><td class="xl24" align="right" xnum="" style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-LEFT-COLOR: windowtext; BORDER-TOP-COLOR: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent;"><font face="宋体">7</font></td></tr><tr height="19" style="HEIGHT: 14.25pt;"><td class="xl24" height="19" style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-LEFT: windowtext 0.5pt solid; BORDER-TOP-COLOR: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; HEIGHT: 14.25pt; BACKGROUND-COLOR: transparent;"><font face="宋体">D</font></td><td class="xl24" align="right" xnum="" style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-LEFT-COLOR: windowtext; BORDER-TOP-COLOR: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent;"><font face="宋体">1</font></td><td class="xl24" style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-LEFT-COLOR: windowtext; BORDER-TOP-COLOR: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent;"><font face="宋体"> </font></td><td class="xl24" align="right" xnum="" style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-LEFT-COLOR: windowtext; BORDER-TOP-COLOR: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent;"><font face="宋体">3</font></td><td class="xl24" align="right" xnum="" style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-LEFT-COLOR: windowtext; BORDER-TOP-COLOR: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent;"><font face="宋体">4</font></td><td class="xl24" align="right" xnum="" style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-LEFT-COLOR: windowtext; BORDER-TOP-COLOR: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent;"><font face="宋体">6</font></td><td class="xl24" align="right" xnum="" style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-LEFT-COLOR: windowtext; BORDER-TOP-COLOR: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent;"><font face="宋体">5</font></td><td class="xl24" align="right" xnum="" style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-LEFT-COLOR: windowtext; BORDER-TOP-COLOR: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent;"><font face="宋体">7</font></td></tr><tr height="19" style="HEIGHT: 14.25pt;"><td class="xl24" height="19" style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-LEFT: windowtext 0.5pt solid; BORDER-TOP-COLOR: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; HEIGHT: 14.25pt; BACKGROUND-COLOR: transparent;"><font face="宋体">E</font></td><td class="xl24" style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-LEFT-COLOR: windowtext; BORDER-TOP-COLOR: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent;"><font face="宋体"> </font></td><td class="xl24" style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-LEFT-COLOR: windowtext; BORDER-TOP-COLOR: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent;"><font face="宋体"> </font></td><td class="xl24" style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-LEFT-COLOR: windowtext; BORDER-TOP-COLOR: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent;"><font face="宋体"> </font></td><td class="xl24" style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-LEFT-COLOR: windowtext; BORDER-TOP-COLOR: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent;"><font face="宋体"> </font></td><td class="xl24" align="right" xnum="" style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-LEFT-COLOR: windowtext; BORDER-TOP-COLOR: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent;"><font face="宋体">7</font></td><td class="xl24" align="right" xnum="" style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-LEFT-COLOR: windowtext; BORDER-TOP-COLOR: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent;"><font face="宋体">6</font></td><td class="xl24" align="right" xnum="" style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-LEFT-COLOR: windowtext; BORDER-TOP-COLOR: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent;"><font face="宋体">5</font></td></tr><tr height="19" style="HEIGHT: 14.25pt;"><td class="xl24" height="19" style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-LEFT: windowtext 0.5pt solid; BORDER-TOP-COLOR: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; HEIGHT: 14.25pt; BACKGROUND-COLOR: transparent;"><font face="宋体">F</font></td><td class="xl24" style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-LEFT-COLOR: windowtext; BORDER-TOP-COLOR: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent;"><font face="宋体"> </font></td><td class="xl24" style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-LEFT-COLOR: windowtext; BORDER-TOP-COLOR: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent;"><font face="宋体"> </font></td><td class="xl24" style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-LEFT-COLOR: windowtext; BORDER-TOP-COLOR: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent;"><font face="宋体"> </font></td><td class="xl24" style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-LEFT-COLOR: windowtext; BORDER-TOP-COLOR: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent;"><font face="宋体"> </font></td><td class="xl24" align="right" xnum="" style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-LEFT-COLOR: windowtext; BORDER-TOP-COLOR: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent;"><font face="宋体">5</font></td><td class="xl24" align="right" xnum="" style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-LEFT-COLOR: windowtext; BORDER-TOP-COLOR: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent;"><font face="宋体">7</font></td><td class="xl24" align="right" xnum="" style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-LEFT-COLOR: windowtext; BORDER-TOP-COLOR: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent;"><font face="宋体">6</font></td></tr></tbody></table></p><p>1.任何一个偶环可以被三置换含二个块的偶环</p><p>2.A行代表所有块的初始位置</p><p>3.设系统有三个偶环,经三置换分别分解后,变换成三个环:C(21),C(43),C(65),见B行</p><p>4.选B行的c(21)c(43)的三个块2，1，4进行一次三置换，生成环C（413），见C行</p><p>5.对C行的C（413）进行一次三置换，则1，2，3，4块全部回到初始位置，余下独偶环C（65），见D行，至此证明偶数个偶环可以被三置换完全分解</p><p>6.若分解环C（65）显然少了一个元素，所以引进块7</p><p>7.对D行的块6，5，7进行一次方向为右的三置换，生成环C（75），见E行</p><p>8.对D行的块6，5，7进行一次方向为左的三置换，生成环C（76），见F行</p><p>9.显然第7和第8个步骤偿试了所有的三置换可能,由此证明奇数个偶环不能被三置换完全分解</p><p><strong>说明</strong></p><p>任意奇数个偶环,均可被三置换分别分解成C(ab)形式,再被三置换二二分解掉,最后余下一个独偶环C(a'b')不能分解，这种现现象被称为扰动，是N阶定律扰动关系描述的根基</p>
[此贴子已经被作者于2007-3-13 9:11:21编辑过]
<p><strong>五。证明置换与置换方向无关</strong></p><p>招标中。。。</p><p>难度：很小</p><p>说明：置换有以下几个无关</p><p>1。位置无关：已证明</p><p>2。色向无关：已证明</p><p>3。置换方向无关：未证明</p>
[此贴子已经被作者于2007-3-13 10:33:47编辑过]
<p><strong>六。证明位移簇任意四个块的一次四轮换改变簇的当前扰动状态</strong></p><p>招标中。。。</p><p>难度：较大，也可能出奇地小，要看使用的方法</p><p>说明：</p><p>以上命题是N阶定律的基石，如果被证伪，N阶定律将立即崩溃。</p>
[此贴子已经被作者于2007-3-27 19:40:52编辑过]
<p><strong>七。证明魔方每个位移簇都可以独立三置换</strong></p><p>招标中。。。</p><p>难度：可能很大，没有偿试过</p><p>说明：</p><p>这又是一个未做一般性证明而被晋遍认可的潜规则，第六和第七命题任何一个被证伪，将颠覆对N阶定律</p>
[此贴子已经被作者于2007-3-27 19:42:18编辑过]
<p>哈哈，逼你乔迁新居，是我本意，只不过招数太狠。此目的已经达到，我将隐退。</p>拜托删除过火的帖子。
[此贴子已经被作者于2007-3-10 16:06:05编辑过]
<p>2楼的“4.C行代表对B行的块<strong><font color="#0033ff">8,3,2,1</font></strong>进行一次向左的四轮换,生成环C(4,1,2,6,7,8)”</p><p>是否应为“4.C行代表对B行的块<strong><font color="#0033ff">2，3，8，5</font></strong>进行一次向左的四轮换,生成环C(4,1,2,6,7,8)”？</p> <p>乌兄说得对，有笔误，已更正，谢谢</p>