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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 = 7, rank = 4 (dimension = 3)
List of the 11 non-degenerate (uniform) representatives of IC(7,4), ordered by the RevLex-Index.
The numbers above the signs indicate the elements of the corresponding basis.
11112111211212311121121231121231234
22233223323344422332334442334445555
33444344455555534445555556666666666
45555666666666677777777777777777777
IC(7,4, 1) = ++++++++++++++++++++++++-++++------
IC(7,4, 2) = +++++++++++++++++++++++++++-------+
IC(7,4, 3) = ++++++++++++++++++++++++++++--+--++
IC(7,4, 4) = ++++++++++++++++++++++++++++-++---+
IC(7,4, 5) = ++++++++++++++++++++++++++++-++--++
IC(7,4, 6) = ++++++++++++++++++++++++++++++-----
IC(7,4, 7) = ++++++++++++++++++++++++++++++-+---
IC(7,4, 8) = ++++++++++++++++++++++++++++++++---
IC(7,4, 9) = +++++++++++++++++++++++++++++++++--
IC(7,4,10) = ++++++++++++++++++++++++++++++++++-
IC(7,4,11) = +++++++++++++++++++++++++++++++++++