= Two-domain-wall degeneracy of a Potts ring
{title2=$d_1=Q(Q-1)\binom L2$}
For $Q,L\ge2$, a <periodic Potts chain> has $Q$ uniform <ground states> with <energy> $-JL$. A single <domain wall> cannot close around the ring. Its <first excited states> have two <domain walls> and <energy> $-JL+2J$. Choose the wall bonds in $\binom L2$ ways and assign distinct states to the two resulting arcs in $Q(Q-1)$ ways. This proves the displayed <degeneracy factor> without identifying globally relabelled configurations.
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