1,9

A combinatorial configuration of type (n_3) consists of an (abstract) set of n points together with a set of n triples of points, called lines, such that each point belongs to 3 lines and each line contains 3 points.

Interchanging the roles of points and lines gives the dual configuration. A configuration is self-dual if there is an isomorphism from it to its dual.

A. Betten, G. Brinkmann and T. Pisanski, Counting symmetric configurations v_3, Discrete Appl. Math., 99 (2000), 331-338.

Pisanski, T.; Boben, M.; Marusic, D.; Orbanic, A.; and Graovac, A. The 10-cages and derived configurations. Discrete Math. 275 (2004), 265-276.

Example: the Fano plane is the only (7_3) configuration and is self-dual. It contains 7 points 1,2,...7 and 7 triples, 124, 235, 346, 457, 561, 672, 713.

The unique (8_3) configuration is also self-dual. It consists of the triples 125, 148, 167, 236, 278, 347, 358, 456.

Cf. A001403 (configurations (n_3), with many further references), A099999, A023994.

See also A005787, A000698, A098702, A098804, A098822, A098841, A098851, A098852, A098854

Sequence in context: A131433 A110713 A098702 this_sequence A110158 A105660 A056681

Adjacent sequences: A099998 A099999 A100000 this_sequence A100002 A100003 A100004

nonn,nice,hard

N. J. A. Sloane (njas(AT)research.att.com), Nov 05 2004

a(1)-a(18) from the Betten, Brinkmann and Pisanski article.

a(19) from the Pisanski et al. article.