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Number of chirotopes resulting from realizable uniform oriented matroids of rank 3 over a ground set of n elements modulo permutations.
1

%I #10 Jul 07 2015 17:36:03

%S 1,3,4,41,706,28287

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

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

%C 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.

%D J. Brunnemann and D. Rideout, "Oriented matroids—combinatorial structures underlying loop quantum gravity", Class.Quant.Grav. 27, 205008 (2010).

%D J. Richter-Gebert, "On the Realizability Problem of Combinatorial Geometries - Decision Methods", Ph.D. thesis, TH-Darmstadt 1992, 144 pages.

%Y Cf. A018242.

%K nonn,more

%O 3,2

%A Johannes Brunnemann (jbrunnem(AT)math.upb.de) and _David Rideout_, Nov 19 2010