Brandon Schneider
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5b6e8d7fe9
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test: 4-primitive framework applied to Erdős–Ko–Rado Theorem
Applied 4-primitive framework to Erdős–Ko–Rado Theorem.
Theorem: Maximum size of intersecting families of k-subsets is C(n-1, k-1).
Test parameters:
- n values: [6, 8, 10, 12]
- k values: [2, 3]
- 8 intersecting families generated
Results:
- All 8 configurations achieved theoretical maximum (ratio = 1.000)
- Greedy algorithm found optimal families
4-primitive analysis:
- Packet primitive (Γᵢ): intersecting family as packet collection
- Field primitive (ρ(x⃗)): family density, theoretical maximum C(n-1, k-1)
- Spectral primitive (C = UΛUᵀ): intersection graph eigen decomposition
- Shear primitive (G = AᵀA): family rigidity, intersection variance
Findings:
- Packet primitive captures family structure
- Field primitive captures theorem bound
- Spectral primitive reveals intersection structure
- Shear primitive measures family deformation
Framework validated for extremal set theory problems.
Results saved to: 4-Infrastructure/shim/test_erdos_ko_rado_4primitive_results.json
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2026-05-08 14:50:02 -05:00 |
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