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Glossary |
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 = 9, rank = 8 (dimension = 7)
List of the 7 representatives of IC(9,8), ordered by the RevLex-Index.
The numbers above the signs indicate the elements of the corresponding basis.
111111112
222222233
333333444
444445555
555566666
666777777
778888888
899999999
IC(9,8,1) = +++++++++
IC(9,8,2) = 0++++++++
IC(9,8,3) = 00+++++++
IC(9,8,4) = 000++++++
IC(9,8,5) = 0000+++++
IC(9,8,6) = 00000++++
IC(9,8,7) = 000000+++