

A001403


Number of combinatorial configurations of type (n_3).


12



0, 0, 0, 0, 0, 0, 1, 1, 3, 10, 31, 229, 2036, 21399, 245342, 3004881, 38904499, 530452205, 7640941062
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OFFSET

1,9


COMMENTS

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.


REFERENCES

Bokowski and Sturmfels, Comput. Synthetic Geom., Lect Notes Math. 1355, p. 41.
CRC Handbook of Combinatorial Designs, 1996, p. 255.
Branko Grünbaum, Configurations of Points and Lines, Graduate Studies in Mathematics, 103 (2009), American Mathematical Society.
D. Hilbert and S. CohnVossen, Geometry and the Imagination, Chelsea, NY, 1952, Ch. 3.
F. Levi, Geometrische Konfigurationen, Hirzel, Leipzig, 1929.
Pisanski, T. and Randic, M., Bridges between Geometry and Graph Theory, in Geometry at Work: Papers in Applied Geometry (Ed. C. A. Gorini), M.A.A., Washington, DC, pp. 174194, 2000.
B. Polster, A Geometrical Picture Book, Springer, 1998, p. 28.
Sturmfels and White, Rational realizations..., in H. Crapo et al. editors, Symbolic Computation in Geometry, IMA preprint, Univ. Minn., 1988.
David Wells, Penguin Dictionary of Curious and Interesting Geometry, 1991, p. 72.


LINKS



EXAMPLE

The Fano plane is the only (7_3) configuration. It contains 7 points 1,2,...,7 and 7 triples, 124, 235, 346, 457, 561, 672, 713.
The unique (8_3) configuration consists of the triples 125, 148, 167, 236, 278, 347, 358, 456.
There are three configurations (9_3), one of which arises from Pappus's theorem. See the World of Mathematics "Configuration" link above for diagrams of all three.
There are nine configurations (10_3), one of which is the familiar configuration arising from Desargues's theorem (see Loy illustration).


CROSSREFS



KEYWORD

nonn,nice,hard,more


AUTHOR



EXTENSIONS

Von Sterneck has 228 instead of 229. His error was corrected by Gropp. The n=15 term was computed by Dieter and Anton Betten, University of Kiel.
a(16)a(18) from the Betten, Brinkmann and Pisanski article.
a(19) from the Pisanski et al. article.


STATUS

approved



