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>
This commit is contained in:
Binary file not shown.
@@ -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}
|
||||
|
||||
|
||||
Reference in New Issue
Block a user