Hooks divisible by the abacus modulus
= Hooks divisible by the abacus modulus
Hooks of $\lambda$ whose lengths are divisible by $e$ correspond bijectively to hooks in the $e$-quotient. A bead-gap pair on one runner with distance $eh$ becomes a bead-gap pair of distance $h$ in that runner partition, and hook removal commutes with this correspondence.
= Abacus divisible-hook correspondence
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