Add bridge-derived census (n=6..10) to the disjunction section

Cross-tabulate bridge-derived vs intertwining-tree coverage: the bridge-derived share falls from 100% (n=6) to 62.7% (n=10), the disjunction never relies on it alone, and the "neither" column is identically zero throughout. Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
2026-06-19 02:27:49 -04:00
parent b1d681f39e
commit d9007c8697
7 changed files with 191 additions and 49 deletions
@@ -0,0 +1,84 @@
+"""Survey: for each n, how many maximal planar graphs (plane-triangulation
+iso classes) are *bridge-derived* level graphs of some Even Level Graph.
+
+Bridge-derivedness is decided exhaustively via the backward bridge-switch
+orbit (see small_n_probe.is_bridge_derived): a triangulation G is
+bridge-derived iff some valid parity partition L of G admits an Even Level
+Graph (parity L) in G's backward bridge-orbit. Feasible only at small n.
+
+Also cross-tabulates against the intertwining-tree property so the two
+covering families in the disjunction conjecture can be compared.
+
+Usage: python3 bridge_derived_survey.py [n_max]   (default 11)
+"""
+import sys
+import os
+import time
+sys.path.insert(0, '/Users/didericis/Code/math-research/papers/'
+                'level_resolutions_of_maximal_planar_graphs/experiments')
+sys.path.insert(0, os.path.dirname(os.path.abspath(__file__)))
+from triangulation_gen import enumerate_all_triangulations
+from small_n_probe import is_bridge_derived
+from test_disjunction import is_intertwining_tree
+
+
+def survey_n(n):
+    t0 = time.time()
+    tris = enumerate_all_triangulations(n)
+    n_bridge = 0
+    n_inter = 0
+    n_bridge_and_inter = 0
+    n_bridge_only = 0
+    n_inter_only = 0
+    n_neither = 0
+    for G in tris:
+        bd = is_bridge_derived(G)
+        it = is_intertwining_tree(G)[0]
+        if bd:
+            n_bridge += 1
+        if it:
+            n_inter += 1
+        if bd and it:
+            n_bridge_and_inter += 1
+        elif bd:
+            n_bridge_only += 1
+        elif it:
+            n_inter_only += 1
+        else:
+            n_neither += 1
+    return {
+        'n': n,
+        'total': len(tris),
+        'bridge': n_bridge,
+        'inter': n_inter,
+        'bridge_and_inter': n_bridge_and_inter,
+        'bridge_only': n_bridge_only,
+        'inter_only': n_inter_only,
+        'neither': n_neither,
+        'elapsed': time.time() - t0,
+    }
+
+
+def main():
+    n_max = int(sys.argv[1]) if len(sys.argv) > 1 else 11
+    rows = []
+    print(f'{"n":>3} {"total":>7} {"bridge-deriv":>13} {"%":>6} '
+          f'{"inter":>7} {"b&i":>6} {"b-only":>7} {"i-only":>7} '
+          f'{"neither":>8} {"sec":>7}', flush=True)
+    for n in range(6, n_max + 1):
+        r = survey_n(n)
+        rows.append(r)
+        pct = 100.0 * r['bridge'] / r['total'] if r['total'] else 0.0
+        print(f'{r["n"]:>3} {r["total"]:>7} {r["bridge"]:>13} {pct:>5.1f}% '
+              f'{r["inter"]:>7} {r["bridge_and_inter"]:>6} '
+              f'{r["bridge_only"]:>7} {r["inter_only"]:>7} '
+              f'{r["neither"]:>8} {r["elapsed"]:>6.1f}', flush=True)
+        if r['neither']:
+            print(f'  *** {r["neither"]} triangulation(s) at n={n} are '
+                  f'NEITHER bridge-derived nor intertwining trees ***',
+                  flush=True)
+    return rows
+
+
+if __name__ == '__main__':
+    main()