I'm trying to understand Young tableaux and was making some exercises.
I'm a bit confused with the following question Given a tensor $B^{ijk}$ where $B^{ijk} = -B^{jik}$ and $B^{ijk} + B^{kij} + B^{jki} = 0$, draw the Young tableau.
I can see that the first two indices are anti-symmetric from the first condition, but I'm confused on the second. It seems to me that it says that the tensor is symmetric with respect to interchange of the first and last indices as well as the second and third.