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Topic: Complexity of hierarchical structures
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Posts: 1
From: Grand Rapids
Registered: 4/19/09
Complexity of hierarchical structures
Posted: Apr 19, 2009 3:43 PM
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I am trying to find an explicit formula for a series I derived. The series describes the complexity of a hierarchical structure in this way:
Say you have a three word phrase and want to see how many parts you can break it into, the complexity is how many ways you can break up the phrase. Order doesn't matter. For example, if your phrase is "the black dog", you could break it up into "the black dog", "the black", "the dog", "black dog", "the", "black", "dog". So, there are 7 ways to break up a 3 letter phrase. Therefore, the complexity of a 3 word phrase is 7. I found that the complexity of any n-word phrase is given by the sum of i=1 to n of n!/i!. Does any one know or know how to find an explicit formula for this series?

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