A082790 Number of nonisomorphic configurations of degree >= 2 (or generators) of n triples in Steiner triple systems.

0, 0, 0, 1, 1, 5, 19, 153, 1615, 25180, 479238, 10695820

Offset: 1

Author

T. Forbes (anthony.d.forbes(AT)googlemail.com), May 24 2003

Keywords

• nonn

Comments

A configuration is a set of triples (of points) where every pair of points occurs in at most one triple. (A Steiner triple system is a set of triples where every pair occurs exactly once; thus configurations are often called partial Steiner triple systems). The triples are also called blocks.

A 'generator' is 'a configuration where every point occurs in at least two blocks'. The term refers to the work of Horak, Phillips, Wallis & Yucas, who show that the number of occurrences of a configuration in a Steiner triple system is expressible as a linear form in the numbers of occurrences of the generators.

If you relax the restriction on the number of times a pair of points can occur in a configuration - so that a configuration is just any multi-set of triples - then we get A050913.

References

• Forbes, Grannell & Griggs, 'Configurations and trades in Steiner triple systems', in preparation.
• Mike Grannell and Terry Griggs, 'Configurations in Steiner triple systems', in Combinatorial Designs and their Applications, Chapman & Hall, CRC Research Notes in Math. 403 (1999), 103-126.
• Horak, P., Phillips, N. K. C., Wallis, W. D. and Yucas, J. L., Counting frequencies of configurations in Steiner triple systems. Ars Combin. 46 (1997), 65-75.

Crossrefs

Cf. A082789, A050913.