

A082790


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


3



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

1,6


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 multiset 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), 103126.
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), 6575.


LINKS

Table of n, a(n) for n=1..12.


CROSSREFS

Cf. A082789, A050913.
Sequence in context: A187018 A193287 A027269 * A145935 A024529 A106991
Adjacent sequences: A082787 A082788 A082789 * A082791 A082792 A082793


KEYWORD

nonn


AUTHOR

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


STATUS

approved



