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Jump to navigationJump to search→Symmetric Group S<sub>3</sub>: format table
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<br>
−<pre>
−Permutations or Substitutions in Sym_{A, B, C}
−o---------o---------o---------o---------o---------o---------o
−| | | | | | |
−| e | f | g | h | i | j |
−| | | | | | |
−o=========o=========o=========o=========o=========o=========o
−| | | | | | |
−| A B C | A B C | A B C | A B C | A B C | A B C |
−| | | | | | |
−| | | | | | | | | | | | | | | | | | | | | | | | |
−| v v v | v v v | v v v | v v v | v v v | v v v |
−| | | | | | |
−| A B C | C A B | B C A | A C B | C B A | B A C |
−| | | | | | |
−o---------o---------o---------o---------o---------o---------o
−</pre>
~+~+~+~
~+~+~+~
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===Symmetric Group S<sub>3</sub>===
===Symmetric Group S<sub>3</sub>===
−<br>
<br>
{| align="center" border="1" cellpadding="8" cellspacing="0" style="background:#f8f8ff; text-align:center; width:90%"
{| align="center" border="1" cellpadding="8" cellspacing="0" style="background:#f8f8ff; text-align:center; width:90%"
−|+ <math>\text{Permutations or Substitutions in}~ \operatorname{Sym} \{ \mathrm{A}, \mathrm{B}, \mathrm{C} \}</math>
+|+ <math>\text{Permutation Substitutions in}~ \operatorname{Sym} \{ \mathrm{A}, \mathrm{B}, \mathrm{C} \}</math>
|- style="background:#f0f0ff"
|- style="background:#f0f0ff"
| width="16%" | <math>\operatorname{e}</math>
| width="16%" | <math>\operatorname{e}</math>
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|
|
<math>\begin{matrix}
<math>\begin{matrix}
−\mathrm{A} & \mathrm{B} & \mathrm{C}
−\\[4pt]
+\\[3pt]
−\downarrow & \downarrow & \downarrow
−\\[4pt]
+\\[6pt]
−\mathrm{A} & \mathrm{B} & \mathrm{C}
−\\[4pt]
−\end{matrix}</math>
\end{matrix}</math>
|
|
<math>\begin{matrix}
<math>\begin{matrix}
−\mathrm{A} & \mathrm{B} & \mathrm{C}
−\\[4pt]
+\\[3pt]
−\downarrow & \downarrow & \downarrow
−\\[4pt]
+\\[6pt]
−\mathrm{C} & \mathrm{A} & \mathrm{B}
−\\[4pt]
−\end{matrix}</math>
\end{matrix}</math>
|
|
<math>\begin{matrix}
<math>\begin{matrix}
−\mathrm{A} & \mathrm{B} & \mathrm{C}
−\\[4pt]
+\\[3pt]
−\downarrow & \downarrow & \downarrow
−\\[4pt]
+\\[6pt]
−\mathrm{B} & \mathrm{C} & \mathrm{A}
−\\[4pt]
−\end{matrix}</math>
\end{matrix}</math>
|
|
<math>\begin{matrix}
<math>\begin{matrix}
−\mathrm{A} & \mathrm{B} & \mathrm{C}
−\\[4pt]
+\\[3pt]
−\downarrow & \downarrow & \downarrow
−\\[4pt]
+\\[6pt]
−\mathrm{A} & \mathrm{C} & \mathrm{B}
−\\[4pt]
−\end{matrix}</math>
\end{matrix}</math>
|
|
<math>\begin{matrix}
<math>\begin{matrix}
−\mathrm{A} & \mathrm{B} & \mathrm{C}
−\\[4pt]
+\\[3pt]
−\downarrow & \downarrow & \downarrow
−\\[4pt]
+\\[6pt]
−\mathrm{C} & \mathrm{B} & \mathrm{A}
−\\[4pt]
−\end{matrix}</math>
\end{matrix}</math>
|
|
<math>\begin{matrix}
<math>\begin{matrix}
−\mathrm{A} & \mathrm{B} & \mathrm{C}
−\\[4pt]
+\\[3pt]
−\downarrow & \downarrow & \downarrow
−\\[4pt]
+\\[6pt]
−\mathrm{B} & \mathrm{A} & \mathrm{C}
−\\[4pt]
−\end{matrix}</math>
\end{matrix}</math>
|}
|}
