Two-quotient tower of the partition three-one
= Two-quotient tower of the partition three-one
{title2=$TQ_2(3,1)$}
The nonempty levels of the 2-quotient tower of $(3,1)$ are
$$
TQ_2(3,1)_0=((3,1)),\qquad
TQ_2(3,1)_1=((2),\varnothing),
$$
and
$$
TQ_2(3,1)_2=(\varnothing,(1),\varnothing,\varnothing).
$$