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Catalog of Isomorphism Classes of Oriented Matroids
The following table shows the number of 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 |
2 |
4 |
17 |
143 |
4 890 |
461 053 |
95 052 532 |
| rank = 4 (dim = 3) |
1 |
3 |
12 |
206 |
181 472 |
unknown |
unknown |
| rank = 5 (dim = 4) |
1 |
4 |
25 |
6 029 |
unknown |
unknown |
| rank = 6 (dim = 5) |
1 |
5 |
50 |
508 321 |
unknown |
| rank = 7 (dim = 6) |
1 |
6 |
91 |
unknown |
| rank = 8 (dim = 7) |
1 |
7 |
164 |
| rank = 9 (dim = 8) |
1 |
8 |
| rank = 10 (dim = 9) |
1 |
|
Cardinality = 7, rank = 5 (dimension = 4)
List of the 25 representatives of IC(7,5), ordered by the RevLex-Index.
The numbers above the signs indicate the elements of the corresponding basis.
111112111121112112123
222233222332233233444
333444334443444555555
445555455556666666666
566666777777777777777
IC(7,5, 1) = +++++++++++++++++++++
IC(7,5, 2) = 0++++++++++++++++++++
IC(7,5, 3) = 0++++++++++0++-++-+--
IC(7,5, 4) = 0++++++++++0+++++++++
IC(7,5, 5) = 0++++++++++0++++++0++
IC(7,5, 6) = 00++++0++++++++++++++
IC(7,5, 7) = 00++++0++++++++0+-+--
IC(7,5, 8) = 00++++0++++++++0+++++
IC(7,5, 9) = 00++++0++++++++0++++0
IC(7,5,10) = 00++++0++++++++00+0++
IC(7,5,11) = 000+++00+++0+++++++++
IC(7,5,12) = 000+++00+++0++++++0++
IC(7,5,13) = 000+++00+++0++++++000
IC(7,5,14) = 000000+++++++++++++++
IC(7,5,15) = 0000000++++++++++++++
IC(7,5,16) = 0000000++++++++0+-+--
IC(7,5,17) = 0000000++++++++0+++++
IC(7,5,18) = 0000000++++++++0++++0
IC(7,5,19) = 00000000+++0+++++++++
IC(7,5,20) = 00000000+++0++++++0++
IC(7,5,21) = 00000000+++0++++++000
IC(7,5,22) = 00000000000++++++++++
IC(7,5,23) = 000000000000+++++++++
IC(7,5,24) = 000000000000++++++0++
IC(7,5,25) = 000000000000000++++++