Original entry on oeis.org
0, 0, 0, 0, 0, 0, 1, 1, 3, 10, 31, 228
Offset: 1
A098702
Number of self-polar configurations of type (n_3).
Original entry on oeis.org
0, 0, 0, 0, 0, 0, 1, 1, 3, 10, 25, 95, 365, 1432, 5799, 24092, 102413, 445363, 1991320
Offset: 1
Example: the Fano plane is the only 7_3 configuration and it is self-polar.
- A. Betten, G. Brinkmann and T. Pisanski, Counting symmetric configurations v_3, Discrete Appl. Math., 99 (2000), 331-338.
- M. Boben et al., Small triangle-free configurations of points and lines, Discrete Comput. Geom., 35 (2006), 405-427.
- T. Pisanski, M. Boben, D. Marušic, A. Orbanic, A. Graovac, The 10-cages and derived configurations, Discrete Math. 275 (2004), 265-276.
a(1)-a(18) from the Betten, Brinkmann and Pisanski article.
a(19) from the Pisanski et al. article.
A098822
Number of cyclic configurations of type (n_3).
Original entry on oeis.org
0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 3, 2, 3, 4, 4, 2, 5, 3
Offset: 1
- A. Betten, G. Brinkmann and T. Pisanski, Counting symmetric configurations v_3, Discrete Appl. Math., 99 (2000), 331-338.
- T. Pisanski, M. Boben, D. Marušic, A. Orbanic, A. Graovac, The 10-cages and derived configurations, Discrete Math. 275 (2004), 265-276.
a(1)-a(18) from the Betten, Brinkmann and Pisanski article.
a(19) from the Pisanski et al. article.
A098804
Number of point-transitive configurations of type (n_3).
Original entry on oeis.org
0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 1, 4, 2, 3, 5, 6, 2, 9
Offset: 1
A098841
Number of disconnected (decomposable) configurations of type (n_3).
Original entry on oeis.org
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 4, 13, 47
Offset: 1
A098851
Number of triangle-free configurations of type (n_3).
Original entry on oeis.org
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 4, 14, 162, 4713, 157211
Offset: 1
- A. Alazemi and A. Betten, Classification of Triangle-Free 22_3 Configurations, International Journal of Combinatorics, Volume 2010, Article ID 767361.
- A. Betten, G. Brinkmann and T. Pisanski, Counting symmetric configurations v_3, Discrete Appl. Math., 99 (2000), 331-338.
- M. Boben et al., Small triangle-free configurations of points and lines, Discrete Comput. Geom., 35 (2006), 405-427.
A098852
Number of triangle-free self-dual configurations of type (n_3).
Original entry on oeis.org
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 2, 6, 40, 307
Offset: 1
A098854
Number of triangle-free self-polar configurations of type (n_3).
Original entry on oeis.org
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 2, 6, 40, 303
Offset: 1
A099999
Number of geometrical configurations of type (n_3).
Original entry on oeis.org
0, 0, 0, 0, 0, 0, 0, 0, 3, 9, 31, 229
Offset: 1
N. J. A. Sloane, following correspondence from Branko Grünbaum and Tomaz Pisanski, Nov 12 2004
The smallest examples occur for n = 9, where there are three configurations, one of which is the configuration arising from Pappus's Theorem (see the World of Mathematics "Configuration" link for drawings of all three).
The configuration arising from Desargues's theorem (see link above to an illustration) is one of the nine configurations for n = 10.
- Many of the following references refer to combinatorial configurations (A001403) rather than geometrical configurations, but are included here in case they are helpful.
- A. Betten and D. Betten, Regular linear spaces, Beitraege zur Algebra und Geometrie, 38 (1997), 111-124.
- 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. See Table 2.2.1, page 69.
- D. Hilbert and S. Cohn-Vossen, 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. 174-194, 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.
- A. Betten and D. Betten, Tactical decompositions and some configurations v_4, J. Geom. 66 (1999), 27-41.
- A. Betten, G. Brinkmann and T. Pisanski, Counting symmetric configurations v_3, Discrete Appl. Math., 99 (2000), 331-338.
- H. Gropp, Configurations and their realization, Discr. Math. 174 (1997), 137-151.
- Jim Loy, Desargues's Theorem
- Jim Loy, The configuration (10_3) arising from Desargues's theorem
- Tomo Pisanski, Papers on configurations
- T. Pisanski, M. Boben, D. Marušic, A. Orbanic and A. Graovac, The 10-cages and derived configurations, Discrete Math. 275 (2004), 265-276.
- B. Sturmfels and N. White, All 11_3 and 12_3 configurations are rational, Aeq. Math., 39 1990 254-260.
- Von Sterneck, Die Config. 11_3, Monat. f. Math. Phys., 5 325-330 1894.
- Von Sterneck, Die Config. 12_3, Monat. f. Math. Phys., 6 223-255 1895.
- Eric Weisstein's World of Mathematics, Configuration.
A100001
Number of self-dual combinatorial configurations of type (n_3).
Original entry on oeis.org
0, 0, 0, 0, 0, 0, 1, 1, 3, 10, 25, 95, 366, 1433, 5802, 24105, 102479, 445577, 1992044
Offset: 1
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.
- A. Betten, G. Brinkmann and T. Pisanski, Counting symmetric configurations v_3, Discrete Appl. Math., 99 (2000), 331-338.
- T. Pisanski, M. Boben, D. Marušic, A. Orbanic, A. Graovac, The 10-cages and derived configurations, Discrete Math. 275 (2004), 265-276.
a(1)-a(18) from the Betten, Brinkmann and Pisanski article.
a(19) from the Pisanski et al. article.
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