= Abacus of a partition
= Partition abacus
{synonym}
An $e$-runner abacus arranges the nonnegative <integers> by their residues modulo $e$ and places beads at the positions in a beta set. Moving a bead up one place on its runner removes a <rim hook> of length $e$, provided the destination is empty.
An abacus represents the <beta set of a partition> by beads at <integer> positions. Positions with the same residue modulo the chosen runner count lie on one runner; moving a bead to an empty position above it represents the corresponding rim-hook removal.
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