Classification of Full-Line and w_3 Configurations in Steiner Triple Systems

623 Steiner triple systems of order 25 are included, used to prove a theorem on full-line configurations. The dataset classifies full n-line configurations for n <= 13 and w_3 configurations for w <= 16, listing each with the size of its minimum generating set. Daniel Heinlein and Patric R. J. Östergård created this dataset for their paper on algorithms and complexity for counting configurations.

Use Cases

• Verify the full-line conjecture for Steiner triple systems of order 25 based on the provided 623 systems and configuration counts.
• Analyze the distribution of minimum generating set sizes for full-line configurations across different n values.
• Study the prevalence of specific configurations like Pasch or mitre within larger Steiner triple systems.

Strengths

• Includes 623 specific Steiner triple systems of order 25 used for a formal theorem proof.
• Provides classifications for all full n-line configurations where n <= 13 and all w_3 configurations where w <= 16.
• Each configuration entry is paired with the concrete size of its minimum generating set.

Limitations

• Column-level documentation is absent; field semantics must be inferred after download.
• Row count is unknown, which may limit suitability assessment.
• Last update date is unknown; freshness unverified.

Provenance

Source

Daniel Heinlein and Patric R. J. Östergård, associated with Aalto University.

Collection Method

Likely generated through computational enumeration and analysis as part of the research for the paper 'Algorithms and Complexity for Counting Configurations in Steiner Triple Systems'.