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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 = 8, rank = 3 (dimension = 2)
List of the 135 non-degenerate (uniform) representatives of IC(8,3), ordered by the RevLex-Index.
The numbers above the signs indicate the elements of the corresponding basis.
11121121231121231234112123123412345112123123412345123456
22332334442334445555233444555566666233444555566666777777
34445555556666666666777777777777777888888888888888888888
IC(8,3, 1) = +++++++++++++++++++-+++++++++-+----+++++++---+-------+--
IC(8,3, 2) = +++++++++++++++++++-+++++++++-+----++++++++--+-------+--
IC(8,3, 3) = +++++++++++++++++++++++++++++-+----++++++--++--+++--+++-
IC(8,3, 4) = +++++++++++++++++++++++++++++-+----++++++-+++---++--+++-
IC(8,3, 5) = +++++++++++++++++++++++++++++-+----++++++-+++--+++--+++-
IC(8,3, 6) = +++++++++++++++++++++++++++++-++---++++-----------------
IC(8,3, 7) = +++++++++++++++++++++++++++++-++---++++++--++---++--+++-
IC(8,3, 8) = +++++++++++++++++++++++++++++-++---++++++-+++---++---++-
IC(8,3, 9) = +++++++++++++++++++++++++++++-++---++++++-+++---++--+++-
IC(8,3, 10) = +++++++++++++++++++++++++++++-++---++++++++--+----------
IC(8,3, 11) = +++++++++++++++++++++++++++++-++---++++++++--+----+-----
IC(8,3, 12) = +++++++++++++++++++++++++++++-++---+++++++++-+----+-----
IC(8,3, 13) = +++++++++++++++++++++++++++++-+++--+++++-+--------------
IC(8,3, 14) = +++++++++++++++++++++++++++++-+++--+++++-++-------------
IC(8,3, 15) = +++++++++++++++++++++++++++++-+++--++++++--++--+++---+++
IC(8,3, 16) = +++++++++++++++++++++++++++++-+++--++++++-+++--+++---+++
IC(8,3, 17) = +++++++++++++++++++++++++++++-+++--++++++-+++--+++--++++
IC(8,3, 18) = +++++++++++++++++++++++++++++-+++--+++++++---+----------
IC(8,3, 19) = +++++++++++++++++++++++++++++-+++--+++++++---+----+-----
IC(8,3, 20) = +++++++++++++++++++++++++++++-+++--++++++++--+----------
IC(8,3, 21) = +++++++++++++++++++++++++++++-+++--++++++++--+----+-----
IC(8,3, 22) = +++++++++++++++++++++++++++++-+++--+++++++++-+-------+--
IC(8,3, 23) = +++++++++++++++++++++++++++++-+++--+++++++++-+----+-----
IC(8,3, 24) = +++++++++++++++++++++++++++++-+++--+++++++++-++---+-----
IC(8,3, 25) = +++++++++++++++++++++++++++++++++--+-------------+----+-
IC(8,3, 26) = +++++++++++++++++++++++++++++++++--+------------++----+-
IC(8,3, 27) = +++++++++++++++++++++++++++++++++--+------------++--++++
IC(8,3, 28) = +++++++++++++++++++++++++++++++++--+-----------+++--++++
IC(8,3, 29) = +++++++++++++++++++++++++++++++++--++-----------++----+-
IC(8,3, 30) = +++++++++++++++++++++++++++++++++--++-+----------+----+-
IC(8,3, 31) = +++++++++++++++++++++++++++++++++--+++--+--++---++---+++
IC(8,3, 32) = +++++++++++++++++++++++++++++++++--+++--+--++--+++---+++
IC(8,3, 33) = +++++++++++++++++++++++++++++++++--+++-++--++---++---++-
IC(8,3, 34) = +++++++++++++++++++++++++++++++++--+++-++--++---++---+++
IC(8,3, 35) = +++++++++++++++++++++++++++++++++--+++-++--++--+++---+++
IC(8,3, 36) = +++++++++++++++++++++++++++++++++--+++-++-+++---++---+++
IC(8,3, 37) = +++++++++++++++++++++++++++++++++--+++-++-+++--+++---+++
IC(8,3, 38) = +++++++++++++++++++++++++++++++++--+++-++-+++--+++--++++
IC(8,3, 39) = +++++++++++++++++++++++++++++++++--+++-++-+++-++++---+++
IC(8,3, 40) = +++++++++++++++++++++++++++++++++--+++-++-+++-++++--++++
IC(8,3, 41) = +++++++++++++++++++++++++++++++++--+++-++-+++-++++-+++++
IC(8,3, 42) = +++++++++++++++++++++++++++++++++--++++--+--------------
IC(8,3, 43) = +++++++++++++++++++++++++++++++++--+++++-+--------------
IC(8,3, 44) = +++++++++++++++++++++++++++++++++--+++++-+---+----------
IC(8,3, 45) = +++++++++++++++++++++++++++++++++--+++++-+---+----+-----
IC(8,3, 46) = +++++++++++++++++++++++++++++++++--+++++-++-------------
IC(8,3, 47) = +++++++++++++++++++++++++++++++++--+++++-++--+----------
IC(8,3, 48) = +++++++++++++++++++++++++++++++++--+++++-++--+----+-----
IC(8,3, 49) = +++++++++++++++++++++++++++++++++--++++++--++----+---++-
IC(8,3, 50) = +++++++++++++++++++++++++++++++++--++++++--++---++---+++
IC(8,3, 51) = +++++++++++++++++++++++++++++++++--++++++--++--+++---+++
IC(8,3, 52) = +++++++++++++++++++++++++++++++++--++++++--++--+++--++++
IC(8,3, 53) = +++++++++++++++++++++++++++++++++--++++++-+++---++---+++
IC(8,3, 54) = +++++++++++++++++++++++++++++++++--++++++-+++--+++---+++
IC(8,3, 55) = +++++++++++++++++++++++++++++++++--++++++-+++--+++--++++
IC(8,3, 56) = +++++++++++++++++++++++++++++++++--+++++++--------------
IC(8,3, 57) = +++++++++++++++++++++++++++++++++--+++++++---+----------
IC(8,3, 58) = +++++++++++++++++++++++++++++++++--+++++++---+----+-----
IC(8,3, 59) = +++++++++++++++++++++++++++++++++--++++++++-------------
IC(8,3, 60) = +++++++++++++++++++++++++++++++++--++++++++--+----------
IC(8,3, 61) = +++++++++++++++++++++++++++++++++--++++++++--+----+-----
IC(8,3, 62) = +++++++++++++++++++++++++++++++++--++++++++--++---------
IC(8,3, 63) = +++++++++++++++++++++++++++++++++--++++++++--++---+-----
IC(8,3, 64) = +++++++++++++++++++++++++++++++++--+++++++++-+----+-----
IC(8,3, 65) = +++++++++++++++++++++++++++++++++--+++++++++-++---+-----
IC(8,3, 66) = +++++++++++++++++++++++++++++++++--+++++++++-++---++----
IC(8,3, 67) = +++++++++++++++++++++++++++++++++--+++++++++-+++--+-----
IC(8,3, 68) = +++++++++++++++++++++++++++++++++--+++++++++-+++--++----
IC(8,3, 69) = +++++++++++++++++++++++++++++++++--+++++++++-+++--+++--+
IC(8,3, 70) = +++++++++++++++++++++++++++++++++--++++++++++++---++----
IC(8,3, 71) = +++++++++++++++++++++++++++++++++--+++++++++++++--++----
IC(8,3, 72) = +++++++++++++++++++++++++++++++++--+++++++++++++--+++--+
IC(8,3, 73) = ++++++++++++++++++++++++++++++++++-+++-----------+------
IC(8,3, 74) = ++++++++++++++++++++++++++++++++++-+++-----------+----+-
IC(8,3, 75) = ++++++++++++++++++++++++++++++++++-+++-++--++--+++--++++
IC(8,3, 76) = ++++++++++++++++++++++++++++++++++-+++-++-+++--+++---+++
IC(8,3, 77) = ++++++++++++++++++++++++++++++++++-+++-++-+++--+++--++++
IC(8,3, 78) = ++++++++++++++++++++++++++++++++++-+++-++-+++-++++---+++
IC(8,3, 79) = ++++++++++++++++++++++++++++++++++-+++-++-+++-++++--++++
IC(8,3, 80) = ++++++++++++++++++++++++++++++++++-++++----------+------
IC(8,3, 81) = ++++++++++++++++++++++++++++++++++-++++----------+----+-
IC(8,3, 82) = ++++++++++++++++++++++++++++++++++-++++----------+----++
IC(8,3, 83) = ++++++++++++++++++++++++++++++++++-++++--+--------------
IC(8,3, 84) = ++++++++++++++++++++++++++++++++++-++++--+---+----------
IC(8,3, 85) = ++++++++++++++++++++++++++++++++++-++++--+---+----+-----
IC(8,3, 86) = ++++++++++++++++++++++++++++++++++-+++++-+--------------
IC(8,3, 87) = ++++++++++++++++++++++++++++++++++-+++++-+---+----------
IC(8,3, 88) = ++++++++++++++++++++++++++++++++++-+++++-+---+----+-----
IC(8,3, 89) = ++++++++++++++++++++++++++++++++++-+++++-++-------------
IC(8,3, 90) = ++++++++++++++++++++++++++++++++++-+++++-++--+----------
IC(8,3, 91) = ++++++++++++++++++++++++++++++++++-+++++-++--+----+-----
IC(8,3, 92) = ++++++++++++++++++++++++++++++++++-+++++-++--++---------
IC(8,3, 93) = ++++++++++++++++++++++++++++++++++-+++++-++--++---+-----
IC(8,3, 94) = ++++++++++++++++++++++++++++++++++-+++++-++--++---++----
IC(8,3, 95) = ++++++++++++++++++++++++++++++++++-++++++--++--+++--++++
IC(8,3, 96) = ++++++++++++++++++++++++++++++++++-++++++-+++--+++---+++
IC(8,3, 97) = ++++++++++++++++++++++++++++++++++-++++++-+++--+++--++++
IC(8,3, 98) = ++++++++++++++++++++++++++++++++++-++++++-+++-++++---+++
IC(8,3, 99) = ++++++++++++++++++++++++++++++++++-++++++-+++-++++--++++
IC(8,3,100) = ++++++++++++++++++++++++++++++++++-++++++-+++-++++-+++++
IC(8,3,101) = ++++++++++++++++++++++++++++++++++-++++++++--++---++----
IC(8,3,102) = ++++++++++++++++++++++++++++++++++-+++++++++-++---+-----
IC(8,3,103) = ++++++++++++++++++++++++++++++++++-+++++++++-++---++----
IC(8,3,104) = ++++++++++++++++++++++++++++++++++-+++++++++-+++--+-----
IC(8,3,105) = ++++++++++++++++++++++++++++++++++-+++++++++-+++--++----
IC(8,3,106) = ++++++++++++++++++++++++++++++++++-+++++++++-+++--+++---
IC(8,3,107) = ++++++++++++++++++++++++++++++++++-++++++++++---++---+++
IC(8,3,108) = ++++++++++++++++++++++++++++++++++-++++++++++--+++---+++
IC(8,3,109) = ++++++++++++++++++++++++++++++++++-++++++++++--+++--++++
IC(8,3,110) = ++++++++++++++++++++++++++++++++++-++++++++++++-------+-
IC(8,3,111) = ++++++++++++++++++++++++++++++++++-++++++++++++---+-----
IC(8,3,112) = ++++++++++++++++++++++++++++++++++-++++++++++++---++----
IC(8,3,113) = ++++++++++++++++++++++++++++++++++-+++++++++++++------+-
IC(8,3,114) = ++++++++++++++++++++++++++++++++++-+++++++++++++--+-----
IC(8,3,115) = ++++++++++++++++++++++++++++++++++-+++++++++++++--++----
IC(8,3,116) = ++++++++++++++++++++++++++++++++++-+++++++++++++--+++---
IC(8,3,117) = ++++++++++++++++++++++++++++++++++-++++++++++++++-+-----
IC(8,3,118) = ++++++++++++++++++++++++++++++++++-++++++++++++++-++----
IC(8,3,119) = ++++++++++++++++++++++++++++++++++-++++++++++++++-+++---
IC(8,3,120) = ++++++++++++++++++++++++++++++++++-++++++++++++++-++++--
IC(8,3,121) = +++++++++++++++++++++++++++++++++++++++++-+++--+++---+++
IC(8,3,122) = +++++++++++++++++++++++++++++++++++++++++++++--+++---+++
IC(8,3,123) = +++++++++++++++++++++++++++++++++++++++++++++--+++--++++
IC(8,3,124) = +++++++++++++++++++++++++++++++++++++++++++++-++++---+++
IC(8,3,125) = +++++++++++++++++++++++++++++++++++++++++++++-++++--++++
IC(8,3,126) = ++++++++++++++++++++++++++++++++++++++++++++++++--++----
IC(8,3,127) = ++++++++++++++++++++++++++++++++++++++++++++++++--+++---
IC(8,3,128) = +++++++++++++++++++++++++++++++++++++++++++++++++-+-----
IC(8,3,129) = +++++++++++++++++++++++++++++++++++++++++++++++++-++----
IC(8,3,130) = +++++++++++++++++++++++++++++++++++++++++++++++++-+++---
IC(8,3,131) = +++++++++++++++++++++++++++++++++++++++++++++++++-++++--
IC(8,3,132) = +++++++++++++++++++++++++++++++++++++++++++++++++++++---
IC(8,3,133) = ++++++++++++++++++++++++++++++++++++++++++++++++++++++--
IC(8,3,134) = +++++++++++++++++++++++++++++++++++++++++++++++++++++++-
IC(8,3,135) = ++++++++++++++++++++++++++++++++++++++++++++++++++++++++