Can a p-core of a partition be reached by repeated stripping of p-rimhooks?

Question

in https://mathoverflow.net/questions/42562 I read : "If you strip p-rimhook after p-rimhook off of a partition, this always results in the same p-core, and the choices don't matter." But I must be misunderstanding this quote, as this counterexample shows: [Mu]={3,3,2,2} has two boxes ( 1,1 and 3,1 ) with hook divisible by 3, but none of these are on the rim, so stripmining stops by lack of 3-rimhooks, and yet [Mu] is not a 3-core.

Answer 1

Rim hooks are not hooks that happen to be on the rim. Rather, if you take any hook, you can connect its extremal boxes along the rim to get a rim hook of the same size. In you example the hook with corner box $(3,1)$ has size three, and the corresponding rim hook has boxes $(3,2),(4,2),(4,1)$, and this $3$-rim hook is indeed removable, reducing the partition to $(3,3,1)$. You can then remove another $3$-rim hook to reduce to $(2,1,1)$, and then no more, so this partition is the $3$-core of $(3,3,2,2)$.