Add per-dual summary table for the six Holton-McKay duals at n=21

Table tab:n21 records, for each of the six duals: not an intertwining tree;
Even Level Graph source (duals 1,2 only); and bridge-switch path length to
an ELG (0,0 for the two ELG-outright cases; 3,1,2,4 for the rest). All six
are bridge-derived; all witnesses step-verified.

Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>
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2026-05-22 11:13:04 -04:00
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@@ -405,7 +405,26 @@ classes: two are Even Level Graphs outright, and the other four are
bridge-derived level graphs. The bridge-switch restriction is what made
the search tractable -- it both shrinks the orbit and guarantees
validity, so any Even Level Graph located in a backward orbit is an
immediate witness.
immediate witness. Table~\ref{tab:n21} records the outcome for each dual.
\begin{table}[ht]
\centering
\begin{tabular}{cccc}
dual & intertwining tree & Even Level Graph source & bridge switches to ELG \\\hline
$0$ & no & -- & $3$ \\
$1$ & no & $10$ & $0$ \\
$2$ & no & $9$ & $0$ \\
$3$ & no & -- & $1$ \\
$4$ & no & -- & $2$ \\
$5$ & no & -- & $4$ \\
\end{tabular}
\caption{The six Holton--McKay duals at $n = 21$, the first triangulations
that are not intertwining trees. Each is a bridge-derived level graph:
duals $1$ and $2$ are Even Level Graphs outright (zero switches), and the
remaining four reach an Even Level Graph in $1$--$4$ bridge switches. All
witnesses are step-verified.}
\label{tab:n21}
\end{table}
\begin{thebibliography}{9}