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Catalog of Isomorphism Classes of Oriented Matroids
The following table shows the number of non-degenerate (uniform) isomorphism classes of oriented matroids
(where card is the cardinality of a simple representative).
Data can be accessed by clicking on the corresponding number (if available):
|
|
| |
card = 2 |
card = 3 |
card = 4 |
card = 5 |
card = 6 |
card = 7 |
card = 8 |
card = 9 |
card = 10 |
| rank = 2 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
| rank = 3 (dim = 2) |
1 |
1 |
1 |
4 |
11 |
135 |
4 382 |
312 356 |
| rank = 4 (dim = 3) |
1 |
1 |
1 |
11 |
2 628 |
9 276 595 |
unknown |
| rank = 5 (dim = 4) |
1 |
1 |
1 |
135 |
9 276 595 |
unknown |
| rank = 6 (dim = 5) |
1 |
1 |
1 |
4 382 |
unknown |
| rank = 7 (dim = 6) |
1 |
1 |
1 |
312 356 |
| rank = 8 (dim = 7) |
1 |
1 |
1 |
| rank = 9 (dim = 8) |
1 |
1 |
| rank = 10 (dim = 9) |
1 |
|
Cardinality = 10, rank = 8 (dimension = 7)
List of the 1 non-degenerate (uniform) representative of IC(10,8), ordered by the RevLex-Index.
The numbers above the signs indicate the elements of the corresponding basis.
111111112111111121111112111112111121112112123
222222233222222332222233222233222332233233444
333333444333334443333444333444334443444555555
444445555444455554445555445555455556666666666
555566666555666665566666566666777777777777777
666777777667777776777777888888888888888888888
778888888788888889999999999999999999999999999
899999999aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa
IC(10,8,1) = +++++++++++++++++++++++++++++++++++++++++++++