A063851 - OEIS

%I #29 Mar 31 2023 14:16:46

%S 1,1,1,1,1,1,1,1,1,4,1,1,1,11,11,1,1,1,135,2628,135,1,1,1,4382,

%T 9276601,9276601,4382,1,1,1,312356

%N Triangle T(n,k) (n >= 3, k = 1..n-2) read by rows  giving number of nonisomorphic nondegenerate oriented matroids with n points in n-k dimensions.

%H Lukas Finschi, <a href="https://finschi.com/math/om/">Homepage of Oriented Matroids</a> [Gives T(9, 5) = T(9, 6) = 9276595.]

%H L. Finschi and K. Fukuda, <a href="http://www.cccg.ca/proceedings/2001/finschi-1053.ps.gz">Complete combinatorial generation of small point set configurations and hyperplane arrangements</a>, pp. 97-100 in Abstracts 13th Canadian Conference on Computational Geometry (CCCG '01), Waterloo, Aug. 13-15, 2001.

%H Lukas Finschi, <a href="https://doi.org/10.3929/ethz-a-004255224">A Graph Theoretical Approach for Reconstruction and Generation of Oriented Matroids</a>, A dissertation submitted to the Swiss Federal Institute of Technology, Zurich for the degree of Doctor of Mathematics, 2001.

%H Komei Fukuda, Hiroyuki Miyata and Sonoko Moriyama, <a href="https://doi.org/10.1007/s00454-012-9470-0">Complete Enumeration of Small Realizable Oriented Matroids</a>. Discrete Comput. Geom. 49 (2013), no. 2, 359--381. MR3017917. - From _N. J. A. Sloane_, Feb 16 2013 [Beware typos in Table 1.]

%e Triangle begins:

%e 1

%e 1,1,

%e 1,1,1,

%e 1,1,1,4,

%e 1,1,1,11,11,

%e 1,1,1,135,2628,135,

%e 1,1,1,4382,9276601,9276601,4382,

%e 1,1,1,312356,...

%Y For numbers when degenerate matroids are included see A063804. Two rightmost diagonals are A006248 and A222315. Row sums give A063852.

%K nonn,tabl,nice,more

%O 3,10

%A _N. J. A. Sloane_, Aug 26 2001

%E More terms taken from Fukuda et al., 2013. - _N. J. A. Sloane_, Feb 16 2013