A172144 Number of chirotopes resulting from realizable uniform oriented matroids of rank 3 over a ground set of n elements modulo permutations.

1, 3, 4, 41, 706, 28287

Offset: 3

Author

Johannes Brunnemann (jbrunnem(AT)math.upb.de) and David Rideout, Nov 19 2010

Keywords

• nonn
• more

Comments

The above numbers were obtained from random sprinkling of points into S^2.

The first five entries match those constructed from A018242, by explicitly applying each reorientation to a representative chirotope for each class of A018242, and grouping the chirotopes related by a permutation.

References

• J. Brunnemann and D. Rideout, "Oriented matroids—combinatorial structures underlying loop quantum gravity", Class.Quant.Grav. 27, 205008 (2010).
• J. Richter-Gebert, "On the Realizability Problem of Combinatorial Geometries - Decision Methods", Ph.D. thesis, TH-Darmstadt 1992, 144 pages.

Crossrefs

Cf. A018242.