Calculating the Inverse of Juggling Sequences: A Mathematical Perspective

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Homework Statement



Has anyone here read The Mathematics of Juggling by Burkard Polster? I am having a hard time understanding how the inverse of a juggling sequence is calculated on page 27.

For example, the table on the page has 7 rows, and in the fourth row, I'm not sure if that symbol means the inverse of the permutation of the sequence? Or how it is calculated.



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Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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