When interpreting strands as objects in a category, there is one label for each strand. However, we may fix three points $X$, $Y$ and $Z$, and then single strands are specified by paths such as $XY$ or $YZ$. Putting these two qutrit paths from the path table into a $3 \times 3$ matrix, we may select a circulant permutation as shown by assigning equal weights to the paths $XY$, $YZ$ and $ZX$. Circulants are used to form the Koide mass matrices.

Doh. OK, so that braid doesn't go with that particular circulant, but you get the idea.

8 years ago

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