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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 (list; graph; refs; listen; history; text; internal format)
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 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.

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

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Last modified January 23 07:07 EST 2020. Contains 331168 sequences. (Running on oeis4.)