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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 = 9, rank = 7 (dimension = 6)
List of the 91 representatives of IC(9,7), ordered by the RevLex-Index.
The numbers above the signs indicate the elements of the corresponding basis.
111111121111112111112111121112112123
222222332222233222233222332233233444
333334443333444333444334443444555555
444455554445555445555455556666666666
555666665566666566666777777777777777
667777776777777888888888888888888888
788888889999999999999999999999999999
IC(9,7, 1) = ++++++++++++++++++++++++++++++++++++
IC(9,7, 2) = 0+++++++++++++++++++++++++++++++++++
IC(9,7, 3) = 0++++++++++++++0+++--+++--++--+----+
IC(9,7, 4) = 0++++++++++++++0++++-++++-+++-++-+--
IC(9,7, 5) = 0++++++++++++++0++++-++++-0+--+-----
IC(9,7, 6) = 0++++++++++++++0++++++++++++++++++++
IC(9,7, 7) = 0++++++++++++++0++++++++++0++-++-+--
IC(9,7, 8) = 0++++++++++++++0++++++++++0+++++++++
IC(9,7, 9) = 0++++++++++++++0++++++++++0++++++0++
IC(9,7,10) = 00++++++0+++++++++++++++++++++++++++
IC(9,7,11) = 00++++++0++++++++++++0++--++--+----+
IC(9,7,12) = 00++++++0++++++++++++0+++-+++-++-+--
IC(9,7,13) = 00++++++0++++++++++++0+++-+++-0+-+--
IC(9,7,14) = 00++++++0++++++++++++0++++++++++++++
IC(9,7,15) = 00++++++0++++++++++++0++++++++0----+
IC(9,7,16) = 00++++++0++++++++++++0++++++++0+-+--
IC(9,7,17) = 00++++++0++++++++++++0++++++++0+++++
IC(9,7,18) = 00++++++0++++++++++++0++++++++0++++0
IC(9,7,19) = 00++++++0++++++++++++00++-0++-++-+--
IC(9,7,20) = 00++++++0++++++++++++00++-0++-++-0--
IC(9,7,21) = 00++++++0++++++++++++00+++0+++++++++
IC(9,7,22) = 00++++++0++++++++++++00+++0++++++0++
IC(9,7,23) = 00++++++0++++++++++++00+++0++++++000
IC(9,7,24) = 000+++++00+++++0++++++++++++++++++++
IC(9,7,25) = 000+++++00+++++0++++++++++0++-++-+--
IC(9,7,26) = 000+++++00+++++0++++++++++0+++++++++
IC(9,7,27) = 000+++++00+++++0++++++++++0++++++0--
IC(9,7,28) = 000+++++00+++++0++++++++++0++++++0++
IC(9,7,29) = 000+++++00+++++0++++++++++00+-0+-+--
IC(9,7,30) = 000+++++00+++++0++++++++++00++0+++++
IC(9,7,31) = 000+++++00+++++0++++++++++00++0++++0
IC(9,7,32) = 000+++++00+++++0++++++++++000+00+0++
IC(9,7,33) = 0000++++000++++00++++0++++++++++++++
IC(9,7,34) = 0000++++000++++00++++0++++++++0+-+--
IC(9,7,35) = 0000++++000++++00++++0++++++++0+++++
IC(9,7,36) = 0000++++000++++00++++0++++++++0++++0
IC(9,7,37) = 0000++++000++++00++++0++++++++00+0++
IC(9,7,38) = 0000++++000++++00++++0++++++++000000
IC(9,7,39) = 00000+++0000+++000+++00+++0+++++++++
IC(9,7,40) = 00000+++0000+++000+++00+++0++++++0++
IC(9,7,41) = 00000+++0000+++000+++00+++0++++++000
IC(9,7,42) = 00000000++++++++++++++++++++++++++++
IC(9,7,43) = 000000000+++++++++++++++++++++++++++
IC(9,7,44) = 000000000++++++++++++0++--++--+----+
IC(9,7,45) = 000000000++++++++++++0+++-+++-++-+--
IC(9,7,46) = 000000000++++++++++++0++++++++++++++
IC(9,7,47) = 000000000++++++++++++0++++++++0+-+--
IC(9,7,48) = 000000000++++++++++++0++++++++0+++++
IC(9,7,49) = 000000000++++++++++++0++++++++0++++0
IC(9,7,50) = 0000000000+++++0++++++++++++++++++++
IC(9,7,51) = 0000000000+++++0++++++++++0++-++-+--
IC(9,7,52) = 0000000000+++++0++++++++++0+++++++++
IC(9,7,53) = 0000000000+++++0++++++++++0++++++0--
IC(9,7,54) = 0000000000+++++0++++++++++0++++++0++
IC(9,7,55) = 0000000000+++++0++++++++++00+-0+-+--
IC(9,7,56) = 0000000000+++++0++++++++++00++0+++++
IC(9,7,57) = 0000000000+++++0++++++++++00++0++++0
IC(9,7,58) = 00000000000++++00++++0++++++++++++++
IC(9,7,59) = 00000000000++++00++++0++++++++0+-+--
IC(9,7,60) = 00000000000++++00++++0++++++++0+++++
IC(9,7,61) = 00000000000++++00++++0++++++++0++++0
IC(9,7,62) = 00000000000++++00++++0++++++++00+0++
IC(9,7,63) = 00000000000++++00++++0++++++++000000
IC(9,7,64) = 000000000000+++000+++00+++0+++++++++
IC(9,7,65) = 000000000000+++000+++00+++0++++++0++
IC(9,7,66) = 000000000000+++000+++00+++0++++++000
IC(9,7,67) = 000000000000000+++++++++++++++++++++
IC(9,7,68) = 0000000000000000++++++++++++++++++++
IC(9,7,69) = 0000000000000000++++++++++0++-++-+--
IC(9,7,70) = 0000000000000000++++++++++0+++++++++
IC(9,7,71) = 0000000000000000++++++++++0++++++0++
IC(9,7,72) = 00000000000000000++++0++++++++++++++
IC(9,7,73) = 00000000000000000++++0++++++++0+-+--
IC(9,7,74) = 00000000000000000++++0++++++++0+++++
IC(9,7,75) = 00000000000000000++++0++++++++0++++0
IC(9,7,76) = 00000000000000000++++0++++++++00+0++
IC(9,7,77) = 000000000000000000+++00+++0+++++++++
IC(9,7,78) = 000000000000000000+++00+++0++++++0++
IC(9,7,79) = 000000000000000000+++00+++0++++++000
IC(9,7,80) = 000000000000000000000+++++++++++++++
IC(9,7,81) = 0000000000000000000000++++++++++++++
IC(9,7,82) = 0000000000000000000000++++++++0+-+--
IC(9,7,83) = 0000000000000000000000++++++++0+++++
IC(9,7,84) = 0000000000000000000000++++++++0++++0
IC(9,7,85) = 00000000000000000000000+++0+++++++++
IC(9,7,86) = 00000000000000000000000+++0++++++0++
IC(9,7,87) = 00000000000000000000000+++0++++++000
IC(9,7,88) = 00000000000000000000000000++++++++++
IC(9,7,89) = 000000000000000000000000000+++++++++
IC(9,7,90) = 000000000000000000000000000++++++0++
IC(9,7,91) = 000000000000000000000000000000++++++