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Trace: • permutation • number_of_permutations • permutation_group • encryption_key
problem:diagramatic_representation_of_sn

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problem:diagramatic_representation_of_sn [2013/08/21 08:05]
joshuawiscons 		problem:diagramatic_representation_of_sn [2013/08/22 16:35] (current)
bmwoodruff
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   - Formulate a diagrammatic rule for finding the diagram of the inverse of an element of $S_4$.   - Formulate a diagrammatic rule for finding the diagram of the inverse of an element of $S_4$.
   - What is the diagram for the identity.   - What is the diagram for the identity.
-  - Consider $\sigma,\tau\in S_4$ whose diagrams given below. Determine the diagrams for $\sigma\tau$ and $\sigma\tau$. {{ problem:symfourdiagramacdbbadc.png?400 }}+  - Consider $\sigma,\tau\in S_4$ whose diagrams are given below. Determine the diagrams for $\sigma\tau$ and $\sigma\tau$. {{ problem:symfourdiagramacdbbadc.png?400 }}
   - Formulate a diagrammatic rule for finding the diagram of the composition of two elements of $S_4$.   - Formulate a diagrammatic rule for finding the diagram of the composition of two elements of $S_4$.
   - Find a $\sigma \in S_4$ such that $\sigma$ is not the identity but $\sigma^2$ is the identity. Find $5$ more (different) elements in $S_4$ with the same property.   - Find a $\sigma \in S_4$ such that $\sigma$ is not the identity but $\sigma^2$ is the identity. Find $5$ more (different) elements in $S_4$ with the same property.
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 \item Formulate a diagrammatic rule for finding the diagram of the inverse of an element of $S_4$. \item Formulate a diagrammatic rule for finding the diagram of the inverse of an element of $S_4$.
 \item What is the diagram for the identity. \item What is the diagram for the identity.
-\item Consider $\sigma,\tau\in S_4$ whose diagrams given below. Determine the diagrams for $\sigma\tau$ and $\sigma\tau$.+\item Consider $\sigma,\tau\in S_4$ whose diagrams are given below. Determine the diagrams for $\sigma\tau$ and $\sigma\tau$.
 \[\sigma = \begin{tikzpicture}[baseline= (current bounding box.west),vertex/.style={circle,draw=black,fill=blue!15,thick,inner sep=1.5pt}, line width = 2] \[\sigma = \begin{tikzpicture}[baseline= (current bounding box.west),vertex/.style={circle,draw=black,fill=blue!15,thick,inner sep=1.5pt}, line width = 2]
 \foreach \i in {1,2,3,4} { \foreach \i in {1,2,3,4} {
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   * [[wp>Symmetric group]]   * [[wp>Symmetric group]]
  
-{{tag>problem needsreview rjosh}}+{{tag>problem needsreview rjosh rben ben}}
problem/diagramatic_representation_of_sn.1377086741.txt.gz · Last modified: 2013/08/21 08:05 by joshuawiscons

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