Sanity check on spider web calculation For fun I began reading an interesting online paper I found, _Spiders for rank 2 Lie algebras_, and on page $5$ we have the following calculation, akin to a tensor product expansion via bilinearity: $\hskip 0.8in$ !21 However, I believe the $21=6+6+9$ should just be a $12=6+6$, so that $9$ appears only once in the final result as the coefficient of the second web you see. What's going on? (Also, help on more pertinent tags would be appreciated.)

Yes, you are right. I think the fact that $21=6+6+9$ is a coincidence; I think it is more likely that Prof. Kuperberg transposed the digits $1$ and $2$.