clarification in sharding chapter

[eliben]

I may be misunderstanding something, but the Sharding chapter has this paragraph:

https://github.com/jax-ml/scaling-book/blob/main/sharding.md?plain=1#L188

The two sharding options seem to be identical:

• $A[I_X, J] \cdot B[J, K] \to C[I_X, K]$ in the main flow of the text
• $A[I_X, J] \cdot B[J, K] \to C[I_X, K]$ in parenthesis

Yet the text proceeds with "These two choices have different communication costs...", so it's not clear what the two different choices are. Is the second supposed to be C[I, K] on the rhs, or am I missing something obvious?