The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A082789 Number of nonisomorphic configurations of n triples in Steiner triple systems. 5
 1, 2, 5, 16, 56, 282, 1865, 17100, 207697, 3180571 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 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 we 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. If we allow a configuration to be any *set* of triples - i.e. configurations with multiple occurrences of blocks are not allowed, but more than one pair is allowed - then we get A058790. REFERENCES 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 A. D. Forbes, M. J. Grannell and T. S. Griggs, Configurations and trades in Steiner triple systems, Australasian J. Combin. 29 (2004), 75-84. EXAMPLE The five configurations of 3 triples are *---*---* ..... *---*---* ... *---*---* ..... *---*---* ... *---*---* ...... \ .......... ................. * ......... .................. \ ........ .... * ..... * .... * ....... ... / \ ... / ............... .. * . * . * .............. * . / ... \ / .............. /| .* ..... * .............. * | ........................ /. | *---*---*---*---* ..... * . * ........ \ ............. \ .| ......... * ............. * | .......... \ ............. \| ........... * ............. * CROSSREFS Cf. A082790, A050913, A058790. Sequence in context: A052891 A052815 A195931 * A234278 A180678 A072110 Adjacent sequences:  A082786 A082787 A082788 * A082790 A082791 A082792 KEYWORD nonn,nice,more AUTHOR T. Forbes (anthony.d.forbes(AT)googlemail.com), May 24 2003 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified January 28 09:52 EST 2020. Contains 331319 sequences. (Running on oeis4.)