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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 = 3 (dimension = 2)
List of the 143 representatives of IC(7,3), ordered by the RevLex-Index.
The numbers above the signs indicate the elements of the corresponding basis.
11121121231121231234112123123412345
22332334442334445555233444555566666
34445555556666666666777777777777777
IC(7,3, 1) = +++++++++++++++++++-++++++++-----+-
IC(7,3, 2) = +++++++++++++++++++-++++++++--+----
IC(7,3, 3) = +++++++++++++++++++-+++++++++-+----
IC(7,3, 4) = ++++++++++++++++++++++++++--++--+++
IC(7,3, 5) = ++++++++++++++++++++++++++-+++--+++
IC(7,3, 6) = +++++++++++++++++++++++++++++-+----
IC(7,3, 7) = +++++++++++++++++++++++++++++-++---
IC(7,3, 8) = +++++++++++++++++++++++++++++-+++--
IC(7,3, 9) = +++++++++++++++++++++++++++++++++--
IC(7,3, 10) = ++++++++++++++++++++++++++++++++++-
IC(7,3, 11) = +++++++++++++++++++++++++++++++++++
IC(7,3, 12) = 0+++++++++++++++++--+++-++-+++--+++
IC(7,3, 13) = 0+++++++++++++++++--++++-----------
IC(7,3, 14) = 0+++++++++++++++++--+++++----------
IC(7,3, 15) = 0+++++++++++++++++--+++++-+--------
IC(7,3, 16) = 0+++++++++++++++++--+++++-+---+----
IC(7,3, 17) = 0+++++++++++++++++--+++++-++-------
IC(7,3, 18) = 0+++++++++++++++++--+++++-++--+----
IC(7,3, 19) = 0+++++++++++++++++--+++++++-----++-
IC(7,3, 20) = 0+++++++++++++++++--++++++++--+----
IC(7,3, 21) = 0++++++++++++++++++++++-++-+++--+++
IC(7,3, 22) = 0++++++++++++++++++++++-++-+++-++++
IC(7,3, 23) = 0++++++++++++++++++++++++-++--+----
IC(7,3, 24) = 0++++++++++++++++++++++++-++--++---
IC(7,3, 25) = 0+++++++++++++++++++++++++--++--+++
IC(7,3, 26) = 0+++++++++++++++++++++++++-+++---++
IC(7,3, 27) = 0+++++++++++++++++++++++++-+++--+++
IC(7,3, 28) = 0+++++++++++++++++++++++++-+++-++++
IC(7,3, 29) = 0++++++++++++++++++++++++++---+----
IC(7,3, 30) = 0+++++++++++++++++++++++++++-------
IC(7,3, 31) = 0+++++++++++++++++++++++++++--+----
IC(7,3, 32) = 0+++++++++++++++++++++++++++--++---
IC(7,3, 33) = 0++++++++++++++++++++++++++++-++---
IC(7,3, 34) = 0++++++++++++++++++++++++++++++----
IC(7,3, 35) = 0+++++++++++++++++++++++++++++++---
IC(7,3, 36) = 0++++++++++++++++++++++++++++++++--
IC(7,3, 37) = 0+++++++++++++++++++++++++++++++++-
IC(7,3, 38) = 0++++++++++++++++++++++++++++++++++
IC(7,3, 39) = 0++++++++++++++++++0+++++++---+----
IC(7,3, 40) = 0++++++++++++++++++0++++++++-------
IC(7,3, 41) = 0++++++++++++++++++0++++++++--+----
IC(7,3, 42) = 0++++++++++++++++++0++++++++++---++
IC(7,3, 43) = 0++++++++++++++++++0++++++++++--+++
IC(7,3, 44) = 0++++++++++++++++++0++++++++++-++++
IC(7,3, 45) = 0++++++++++++++++++0+++++++++++++++
IC(7,3, 46) = 0++++++0+++++++++---+++--+--++--++-
IC(7,3, 47) = 0++++++0+++++++++---+++-++---+--++-
IC(7,3, 48) = 0++++++0+++++++++---+++-++---+-+++-
IC(7,3, 49) = 0++++++0+++++++++---+++++-++--++--+
IC(7,3, 50) = 0++++++0+++++++++---+++++++---++--+
IC(7,3, 51) = 0++++++0+++++++++---+++++++---+++-+
IC(7,3, 52) = 0++++++0+++++++++---+++++++---+++++
IC(7,3, 53) = 0++++++0++++++++++--+++-++---+---+-
IC(7,3, 54) = 0++++++0++++++++++--+++-++---+--++-
IC(7,3, 55) = 0++++++0++++++++++--+++-++---+--0+-
IC(7,3, 56) = 0++++++0++++++++++--+++-++--++--++-
IC(7,3, 57) = 0++++++0++++++++++--+++-++--++--+++
IC(7,3, 58) = 0++++++0++++++++++--+++-++--++--++0
IC(7,3, 59) = 0++++++0++++++++++--+++++-+---+----
IC(7,3, 60) = 0++++++0++++++++++--+++++-+---0----
IC(7,3, 61) = 0++++++0++++++++++--+++++++--------
IC(7,3, 62) = 0++++++0++++++++++--+++++++------+-
IC(7,3, 63) = 0++++++0++++++++++--+++++++-----++-
IC(7,3, 64) = 0++++++0++++++++++--+++++++---+----
IC(7,3, 65) = 0++++++0++++++++++--++++++++--++--+
IC(7,3, 66) = 0++++++0++++++++++--++++++++--+++-+
IC(7,3, 67) = 0++++++0++++++++++--++++++++--+++++
IC(7,3, 68) = 0++++++0+++++++++++-+++-++---+---+-
IC(7,3, 69) = 0++++++0+++++++++++-+++-++---+---++
IC(7,3, 70) = 0++++++0+++++++++++-+++-++---+---+0
IC(7,3, 71) = 0++++++0+++++++++++-+++-++--++---++
IC(7,3, 72) = 0++++++0+++++++++++-+++-++--++--+++
IC(7,3, 73) = 0++++++0+++++++++++-+++-++--++--0++
IC(7,3, 74) = 0++++++0+++++++++++-+++-++-+++--+++
IC(7,3, 75) = 0++++++0+++++++++++-+++-++-+++-++++
IC(7,3, 76) = 0++++++0+++++++++++-+++-++-+++-0+++
IC(7,3, 77) = 0++++++0+++++++++++-++++--+---+----
IC(7,3, 78) = 0++++++0+++++++++++-++++--+---0----
IC(7,3, 79) = 0++++++0+++++++++++-+++++-+---+----
IC(7,3, 80) = 0++++++0+++++++++++-+++++-+---0----
IC(7,3, 81) = 0++++++0+++++++++++-+++++++--------
IC(7,3, 82) = 0++++++0+++++++++++-+++++++------+-
IC(7,3, 83) = 0++++++0+++++++++++-+++++++------0-
IC(7,3, 84) = 0++++++0+++++++++++-+++++++---+----
IC(7,3, 85) = 0++++++0+++++++++++-+++++++---0----
IC(7,3, 86) = 0++++++0+++++++++++-++++++++--+----
IC(7,3, 87) = 0++++++0+++++++++++-++++++++--++---
IC(7,3, 88) = 0++++++0+++++++++++-++++++++--+0---
IC(7,3, 89) = 0++++++0+++++++++++-++++++++--0----
IC(7,3, 90) = 0++++++0+++++++++++-+++++++++-+++--
IC(7,3, 91) = 0++++++0+++++++++++-+++++++++-+++-+
IC(7,3, 92) = 0++++++0+++++++++++-+++++++++-+++++
IC(7,3, 93) = 0++++++0+++++++++++-+++++++++-++0--
IC(7,3, 94) = 0++++++0+++++++++++-+++++++++-+0---
IC(7,3, 95) = 0++++++0+++++++++++-+++++++++-0++++
IC(7,3, 96) = 0++++++0+++++++0++--+++------+-----
IC(7,3, 97) = 0++++++0+++++++0++--+++++++-----++-
IC(7,3, 98) = 0++++++0+++++++0++--++++++++----++-
IC(7,3, 99) = 0++++++0+++++++0++--++++++++----+++
IC(7,3,100) = 0++++++0+++++++0++--++++++++---++++
IC(7,3,101) = 0++++++0+++++++0++--++++++++--+++++
IC(7,3,102) = 0++++++0+++++++0++--+++++++++---+++
IC(7,3,103) = 0++++++0+++++++0++--+++++++++--++++
IC(7,3,104) = 0++++++0+++++++0++--+++++++++--0+++
IC(7,3,105) = 0++++++0+++++++0++--+++++++++-+++++
IC(7,3,106) = 0++++++0+++++++0++--+++++++0----++-
IC(7,3,107) = 0++++++0+++++++0+0--+++++++-----++-
IC(7,3,108) = 0++++++0+++++++0+0--+++++++++-+++++
IC(7,3,109) = 0++++++0++++++0-+---++++--+---+----
IC(7,3,110) = 0++++++0++++++0-+---++++--+---+---+
IC(7,3,111) = 0++++++0++++++0-+---++++--+---+---0
IC(7,3,112) = 0++++++0++++++0-+---++++--+---0----
IC(7,3,113) = 0++++++0++++++0-+---+++++++---+++++
IC(7,3,114) = 0++++++0++++++0-+---++++++++--+++++
IC(7,3,115) = 0++++++0++++++0-+---+++++++++-+++++
IC(7,3,116) = 0++++++0++++++0-+---++++++++0-+++++
IC(7,3,117) = 0++++++0++++++0-+---+++++0+----+++-
IC(7,3,118) = 0++++++0++++++0-+---+++++0+----++++
IC(7,3,119) = 0++++++0++++++0-+---+++++0+----+++0
IC(7,3,120) = 0++++++0++++++0-+---+++++0++---++++
IC(7,3,121) = 0++++++0++++++0-+---+++++0++--+++++
IC(7,3,122) = 0++++++0++++++0-+---+++++0+0--+++++
IC(7,3,123) = 0++++++0++++++0-+---+++++0+0--0++++
IC(7,3,124) = 0000+++++++++++++++++++++++++-++---
IC(7,3,125) = 0000++++++++++++++++++++++++++++---
IC(7,3,126) = 0000+++++++++++++++++++++++++++++--
IC(7,3,127) = 0000+++++++++++++++++++++++++++++++
IC(7,3,128) = 0000++++++++++++++++++++++++++++++0
IC(7,3,129) = 0000++++++++++++0++++++++++++-++---
IC(7,3,130) = 0000++++++++++++0++++++++++++-+++--
IC(7,3,131) = 0000++++++++++++0++++++++++++++----
IC(7,3,132) = 0000++++++++++++0+++++++++++++++---
IC(7,3,133) = 0000++++++++++++0++++++++++++++++--
IC(7,3,134) = 0000++++++++++++0+++++++++++++++++-
IC(7,3,135) = 0000++++++++++++0++++++++++++0++---
IC(7,3,136) = 0000++++++++++++0++++++++++++0+++--
IC(7,3,137) = 0000++++++++++++0+++++++++++0-++---
IC(7,3,138) = 0000++++++++++++0+++++++++++0-+0---
IC(7,3,139) = 0000++++++++++++0++++++++++0--+----
IC(7,3,140) = 0000++++++++++++0+++++++++0+++0+++0
IC(7,3,141) = 0000000000+++++++++++++++++++++++++
IC(7,3,142) = 0000000000++++++++++++++++++++0++++
IC(7,3,143) = 00000000000000000000+++++++++++++++