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== <u></u>'''Example 1: Square''' == | == <u></u>'''Example 1: Square''' == | ||
| − | '''<br>''' | + | '''A basic example of how to use the theorem is a simple coloring of a two-coloring of a square.<br>''' |
== '''Definitions:''' == | == '''Definitions:''' == | ||
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http://arxiv.org/pdf/1001.0072.pdf | http://arxiv.org/pdf/1001.0072.pdf | ||
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| + | http://math.berkeley.edu/~mbaker/Tucker.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 11:57, 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
A basic example of how to use the theorem is a simple coloring of a two-coloring of a 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:
http://arxiv.org/pdf/1001.0072.pdf
