This dataset contains the classification of full n-line configurations (for all n <= 13, filename: "full_line_config_<n>.txt.gz") and w_3 configurations (for all w <= 16, filename: "w_3_config_<w>.txt.gz") together with the sizes of minimum generating sets. Each file lists "m<s>" so that s is the size of the minimum generating set of the subsequent configuration, which is denoted by writing the points of each of its lines row-wise. For example
m3
0 1 4
0 2 6
0 3 5
1 2 5
1 3 6
2 3 4
4 5 6
is the Fano plane and its minimum generating set has size 3.
Additionally, the file "fulllineconjecture.txt.gz" contains the 623 Steiner triple systems of order 25 (i.e., all rows which contain curly brackets) used in Theorem 7 in the paper below, followed by a row starting with 1 and then describing the number of occurrences of all 179 full n-line configurations for n <= 8, i.e., first the number of occurrences of Pasch configurations, then mitre configurations, then the 5 full 6-line configurations, the 19 full 7-line configurations, and finally the 153 full 8-line configurations contained in the STS(25) in the preceding row. The ordering follows the ordering within the files "full_line_config_<n>.txt.gz". This file is built so that omitting all lines with curly brackets is a valid gap code and results in a prove of said theorem (i.e., zgrep -v "{" fulllineconjecture.txt.gz | gap yields 180).
Further details can be found in the corresponding publication
"Algorithms and Complexity for Counting Configurations in Steiner Triple Systems"
by Daniel Heinlein and Patric R. J. Östergård.
All files are compressed with gzip.
Date made available | 2021 |
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Publisher | Zenodo |
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