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A063851

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.

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, 9276601, 9276601, 4382, 1, 1, 1, 312356

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OFFSET

3,10

LINKS

Lukas Finschi, Homepage of Oriented Matroids [Gives T(9, 5) = T(9, 6) = 9276595.]

L. Finschi and K. Fukuda, Complete combinatorial generation of small point set configurations and hyperplane arrangements, pp. 97-100 in Abstracts 13th Canadian Conference on Computational Geometry (CCCG '01), Waterloo, Aug. 13-15, 2001.

Lukas Finschi, A Graph Theoretical Approach for Reconstruction and Generation of Oriented Matroids, A dissertation submitted to the Swiss Federal Institute of Technology, Zurich for the degree of Doctor of Mathematics, 2001.

Komei Fukuda, Hiroyuki Miyata and Sonoko Moriyama, Complete Enumeration of Small Realizable Oriented Matroids. Discrete Comput. Geom. 49 (2013), no. 2, 359--381. MR3017917. - From N. J. A. Sloane, Feb 16 2013 [Beware typos in Table 1.]

EXAMPLE

Triangle begins:

1,1,

1,1,1,

1,1,1,4,

1,1,1,11,11,

1,1,1,135,2628,135,

1,1,1,4382,9276601,9276601,4382,

1,1,1,312356,...

CROSSREFS

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

KEYWORD

nonn,tabl,nice,more

AUTHOR

EXTENSIONS

More terms taken from Fukuda et al., 2013. - N. J. A. Sloane, Feb 16 2013

STATUS

approved