Four-quotient of the partition three-one (source code)

= Four-quotient of the partition three-one
{title2=$Q_4(3,1)$}

Using the four-bead <beta set> $\{6,3,1,0\}$ and runners ordered by residues $0,1,2,3$, an <abacus of a partition> for $(3,1)$ gives
$$
Q_4(3,1)=(\varnothing,\varnothing,(1),\varnothing).
$$