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<br> | <br> | ||
| − | <u></u>'''<u>Outline</u>''' | + | = <u></u>'''<u>Outline/Title?</u>''' = |
| − | ''<br>'''''Introduction''' | + | == ''<br>'''''Introduction''' == |
In graph theory, it is sometimes necessary to find the number of ways to color the vertices of a polygon. Two theorems that work together to solve this problem are the Polya theorem and Burnside theorem. <br> | In graph theory, it is sometimes necessary to find the number of ways to color the vertices of a polygon. Two theorems that work together to solve this problem are the Polya theorem and Burnside theorem. <br> | ||
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| − | <u></u>'''Example 1: Square''' | + | == <u></u>'''Example 1: Square''' == |
'''<br>''' | '''<br>''' | ||
| − | '''Definitions:''' | + | == '''Definitions:''' == |
*'''Burnside''' | *'''Burnside''' | ||
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'''<br>''' | '''<br>''' | ||
| − | '''Formula:''' | + | == '''Formula:''' == |
*'''show formula''' | *'''show formula''' | ||
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'''<br>''' | '''<br>''' | ||
| − | ''' | + | == '''Proof:''' == |
'''<br>''' | '''<br>''' | ||
| − | '''References and Additional Information''' | + | == '''References and Additional Information''' == |
| − | For further reading on the Polya theorem: | + | For further reading on the Polya theorem: |
| − | http://arxiv.org/pdf/1001.0072.pdf | + | http://arxiv.org/pdf/1001.0072.pdf |
<br> [[2014 Spring MA 375 Walther|Back to MA375 Spring 2014]] | <br> [[2014 Spring MA 375 Walther|Back to MA375 Spring 2014]] | ||
[[Category:MA375Spring2014Walther]] [[Category:Math]] [[Category:Project]] | [[Category:MA375Spring2014Walther]] [[Category:Math]] [[Category:Project]] | ||
Revision as of 11:47, 20 April 2014
We discuss in class colorings of graphs, where adjacent vertices have different colors. Suppose you took the graph to be a polygon and allowed the graph to be reflected and rotated. How many different colorings do you get?
Contents
Outline/Title?
Introduction
In graph theory, it is sometimes necessary to find the number of ways to color the vertices of a polygon. Two theorems that work together to solve this problem are the Polya theorem and Burnside theorem.
Example 1: Square
Definitions:
- Burnside
- Polya
Formula:
- show formula
- breakdown of each element
- relate back to example 1
Proof:
References and Additional Information
For further reading on the Polya theorem:
