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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 = 5 (dimension = 4)
List of the 135 non-degenerate (uniform) representatives of IC(8,5), ordered by the RevLex-Index.
The numbers above the signs indicate the elements of the corresponding basis.
11111211112111211212311112111211212311121121231121231234
22223322233223323344422233223323344422332334442334445555
33344433444344455555533444344455555534445555556666666666
44555545555666666666645555666666666677777777777777777777
56666677777777777777788888888888888888888888888888888888
IC(8,5, 1) = ++++++++++++++++++++++++++++++-+++++++++--++++---+++++++
IC(8,5, 2) = +++++++++++++++++++++++++++++++++-++++-++----+-----+--++
IC(8,5, 3) = +++++++++++++++++++++++++++++++++-+++++++----+-----+--++
IC(8,5, 4) = +++++++++++++++++++++++++++++++++-+++++++-+--+-----+--++
IC(8,5, 5) = +++++++++++++++++++++++++++++++++-+++++++-+--++----+--++
IC(8,5, 6) = +++++++++++++++++++++++++++++++++-+++++++-+-++-----+--++
IC(8,5, 7) = +++++++++++++++++++++++++++++++++-+++++++-+-+++----+--++
IC(8,5, 8) = +++++++++++++++++++++++++++++++++-++++++++----+--------+
IC(8,5, 9) = ++++++++++++++++++++++++++++++++++--++++++----+---------
IC(8,5, 10) = +++++++++++++++++++++++++++++++++++-+-++-+-++----++-++--
IC(8,5, 11) = +++++++++++++++++++++++++++++++++++-++++---+--------++--
IC(8,5, 12) = +++++++++++++++++++++++++++++++++++-++++---++----+--++--
IC(8,5, 13) = +++++++++++++++++++++++++++++++++++-++++-+-+-----+--+---
IC(8,5, 14) = +++++++++++++++++++++++++++++++++++-++++-+-+-----+--++--
IC(8,5, 15) = +++++++++++++++++++++++++++++++++++-++++-+-++-------++--
IC(8,5, 16) = +++++++++++++++++++++++++++++++++++-++++-+-++----+--++--
IC(8,5, 17) = +++++++++++++++++++++++++++++++++++-++++-+-++----++-++--
IC(8,5, 18) = +++++++++++++++++++++++++++++++++++-++++-++++----+--++--
IC(8,5, 19) = +++++++++++++++++++++++++++++++++++-++++++----+---------
IC(8,5, 20) = +++++++++++++++++++++++++++++++++++-++++++-+-----+--+---
IC(8,5, 21) = +++++++++++++++++++++++++++++++++++-++++++-+--++--------
IC(8,5, 22) = +++++++++++++++++++++++++++++++++++-++++++++--------+---
IC(8,5, 23) = +++++++++++++++++++++++++++++++++++-++++++++--++-+------
IC(8,5, 24) = +++++++++++++++++++++++++++++++++++++-++--++++---++-+++-
IC(8,5, 25) = +++++++++++++++++++++++++++++++++++++-++--++++---++++++-
IC(8,5, 26) = +++++++++++++++++++++++++++++++++++++++----+--------+++-
IC(8,5, 27) = +++++++++++++++++++++++++++++++++++++++-+--------------+
IC(8,5, 28) = +++++++++++++++++++++++++++++++++++++++-++-------------+
IC(8,5, 29) = ++++++++++++++++++++++++++++++++++++++++-----+--------++
IC(8,5, 30) = ++++++++++++++++++++++++++++++++++++++++----++-------+++
IC(8,5, 31) = ++++++++++++++++++++++++++++++++++++++++---+--------+++-
IC(8,5, 32) = ++++++++++++++++++++++++++++++++++++++++---++----+--+++-
IC(8,5, 33) = ++++++++++++++++++++++++++++++++++++++++--++++------+++-
IC(8,5, 34) = ++++++++++++++++++++++++++++++++++++++++--++++---++-+++-
IC(8,5, 35) = ++++++++++++++++++++++++++++++++++++++++-+-++----+--++--
IC(8,5, 36) = ++++++++++++++++++++++++++++++++++++++++-+-++----++-++--
IC(8,5, 37) = ++++++++++++++++++++++++++++++++++++++++-+-++--+-+--++--
IC(8,5, 38) = ++++++++++++++++++++++++++++++++++++++++-++++----+--++--
IC(8,5, 39) = ++++++++++++++++++++++++++++++++++++++++-++++----++-++--
IC(8,5, 40) = ++++++++++++++++++++++++++++++++++++++++-++++--+-+--++--
IC(8,5, 41) = ++++++++++++++++++++++++++++++++++++++++-++++--+-++-++--
IC(8,5, 42) = ++++++++++++++++++++++++++++++++++++++++-++++--++++-++--
IC(8,5, 43) = ++++++++++++++++++++++++++++++++++++++++-+++++------++--
IC(8,5, 44) = ++++++++++++++++++++++++++++++++++++++++-+++++---+--++--
IC(8,5, 45) = ++++++++++++++++++++++++++++++++++++++++-+++++---+--+++-
IC(8,5, 46) = ++++++++++++++++++++++++++++++++++++++++-+++++---++-++--
IC(8,5, 47) = ++++++++++++++++++++++++++++++++++++++++-+++++--+++++++-
IC(8,5, 48) = ++++++++++++++++++++++++++++++++++++++++-+++++-+-+--++--
IC(8,5, 49) = ++++++++++++++++++++++++++++++++++++++++-+++++-+-++-++--
IC(8,5, 50) = +++++++++++++++++++++++++++++++++++++++++----++----+--++
IC(8,5, 51) = +++++++++++++++++++++++++++++++++++++++++-+--+--------++
IC(8,5, 52) = +++++++++++++++++++++++++++++++++++++++++-+--+-----+--++
IC(8,5, 53) = +++++++++++++++++++++++++++++++++++++++++-+--++-------++
IC(8,5, 54) = +++++++++++++++++++++++++++++++++++++++++-+--++----+--++
IC(8,5, 55) = +++++++++++++++++++++++++++++++++++++++++-+--++-+--+--++
IC(8,5, 56) = +++++++++++++++++++++++++++++++++++++++++-+-++-------+++
IC(8,5, 57) = +++++++++++++++++++++++++++++++++++++++++-+-++-----+-+++
IC(8,5, 58) = +++++++++++++++++++++++++++++++++++++++++-+-+++-------++
IC(8,5, 59) = +++++++++++++++++++++++++++++++++++++++++-+-+++----+--++
IC(8,5, 60) = +++++++++++++++++++++++++++++++++++++++++-+-+++-+--+--++
IC(8,5, 61) = ++++++++++++++++++++++++++++++++++++++++++-------------+
IC(8,5, 62) = ++++++++++++++++++++++++++++++++++++++++++----+--------+
IC(8,5, 63) = +++++++++++++++++++++++++++++++++++++++++++---++-------+
IC(8,5, 64) = +++++++++++++++++++++++++++++++++++++++++++--+---------+
IC(8,5, 65) = +++++++++++++++++++++++++++++++++++++++++++--+--------++
IC(8,5, 66) = +++++++++++++++++++++++++++++++++++++++++++--+-----+--++
IC(8,5, 67) = +++++++++++++++++++++++++++++++++++++++++++--++-------++
IC(8,5, 68) = +++++++++++++++++++++++++++++++++++++++++++--++----+--++
IC(8,5, 69) = +++++++++++++++++++++++++++++++++++++++++++--++-+--+--++
IC(8,5, 70) = +++++++++++++++++++++++++++++++++++++++++++--+++-------+
IC(8,5, 71) = +++++++++++++++++++++++++++++++++++++++++++--++++--+---+
IC(8,5, 72) = +++++++++++++++++++++++++++++++++++++++++++-++---------+
IC(8,5, 73) = +++++++++++++++++++++++++++++++++++++++++++-++--------++
IC(8,5, 74) = +++++++++++++++++++++++++++++++++++++++++++-++-------+++
IC(8,5, 75) = +++++++++++++++++++++++++++++++++++++++++++-++-----+--++
IC(8,5, 76) = +++++++++++++++++++++++++++++++++++++++++++-++-----+-+++
IC(8,5, 77) = +++++++++++++++++++++++++++++++++++++++++++-++----++-+++
IC(8,5, 78) = +++++++++++++++++++++++++++++++++++++++++++-+++-------++
IC(8,5, 79) = +++++++++++++++++++++++++++++++++++++++++++-+++----+--++
IC(8,5, 80) = +++++++++++++++++++++++++++++++++++++++++++-+++-+--+--++
IC(8,5, 81) = +++++++++++++++++++++++++++++++++++++++++++-+++-+-++--++
IC(8,5, 82) = +++++++++++++++++++++++++++++++++++++++++++-++++-------+
IC(8,5, 83) = +++++++++++++++++++++++++++++++++++++++++++-+++++--+---+
IC(8,5, 84) = +++++++++++++++++++++++++++++++++++++++++++-+++++--+--++
IC(8,5, 85) = +++++++++++++++++++++++++++++++++++++++++++-+++++-++---+
IC(8,5, 86) = +++++++++++++++++++++++++++++++++++++++++++-+++++-++--++
IC(8,5, 87) = ++++++++++++++++++++++++++++++++++++++++++++-----+--+---
IC(8,5, 88) = ++++++++++++++++++++++++++++++++++++++++++++---+-+--+---
IC(8,5, 89) = ++++++++++++++++++++++++++++++++++++++++++++--++--------
IC(8,5, 90) = ++++++++++++++++++++++++++++++++++++++++++++--++-+------
IC(8,5, 91) = ++++++++++++++++++++++++++++++++++++++++++++--+++-------
IC(8,5, 92) = ++++++++++++++++++++++++++++++++++++++++++++--++++------
IC(8,5, 93) = +++++++++++++++++++++++++++++++++++++++++++++-------+---
IC(8,5, 94) = +++++++++++++++++++++++++++++++++++++++++++++-------++--
IC(8,5, 95) = +++++++++++++++++++++++++++++++++++++++++++++----+--+---
IC(8,5, 96) = +++++++++++++++++++++++++++++++++++++++++++++----+--++--
IC(8,5, 97) = +++++++++++++++++++++++++++++++++++++++++++++----++-++--
IC(8,5, 98) = +++++++++++++++++++++++++++++++++++++++++++++--+-+--++--
IC(8,5, 99) = +++++++++++++++++++++++++++++++++++++++++++++--+-++-++--
IC(8,5,100) = +++++++++++++++++++++++++++++++++++++++++++++-++--------
IC(8,5,101) = +++++++++++++++++++++++++++++++++++++++++++++-++-+------
IC(8,5,102) = +++++++++++++++++++++++++++++++++++++++++++++-+++-------
IC(8,5,103) = +++++++++++++++++++++++++++++++++++++++++++++-++++------
IC(8,5,104) = +++++++++++++++++++++++++++++++++++++++++++++-++++--+---
IC(8,5,105) = +++++++++++++++++++++++++++++++++++++++++++++-+++++-----
IC(8,5,106) = +++++++++++++++++++++++++++++++++++++++++++++-+++++-+---
IC(8,5,107) = ++++++++++++++++++++++++++++++++++++++++++++++------+---
IC(8,5,108) = ++++++++++++++++++++++++++++++++++++++++++++++---+--+---
IC(8,5,109) = ++++++++++++++++++++++++++++++++++++++++++++++---+--++--
IC(8,5,110) = ++++++++++++++++++++++++++++++++++++++++++++++---++-++--
IC(8,5,111) = ++++++++++++++++++++++++++++++++++++++++++++++-+-+--++--
IC(8,5,112) = ++++++++++++++++++++++++++++++++++++++++++++++-+-++-++--
IC(8,5,113) = ++++++++++++++++++++++++++++++++++++++++++++++-+++++++--
IC(8,5,114) = ++++++++++++++++++++++++++++++++++++++++++++++-++++++++-
IC(8,5,115) = +++++++++++++++++++++++++++++++++++++++++++++++---------
IC(8,5,116) = +++++++++++++++++++++++++++++++++++++++++++++++--------+
IC(8,5,117) = ++++++++++++++++++++++++++++++++++++++++++++++++--------
IC(8,5,118) = ++++++++++++++++++++++++++++++++++++++++++++++++-------+
IC(8,5,119) = ++++++++++++++++++++++++++++++++++++++++++++++++-+------
IC(8,5,120) = +++++++++++++++++++++++++++++++++++++++++++++++++-------
IC(8,5,121) = +++++++++++++++++++++++++++++++++++++++++++++++++------+
IC(8,5,122) = +++++++++++++++++++++++++++++++++++++++++++++++++--+---+
IC(8,5,123) = +++++++++++++++++++++++++++++++++++++++++++++++++--+--++
IC(8,5,124) = +++++++++++++++++++++++++++++++++++++++++++++++++-++---+
IC(8,5,125) = +++++++++++++++++++++++++++++++++++++++++++++++++-++--++
IC(8,5,126) = ++++++++++++++++++++++++++++++++++++++++++++++++++------
IC(8,5,127) = ++++++++++++++++++++++++++++++++++++++++++++++++++--+---
IC(8,5,128) = +++++++++++++++++++++++++++++++++++++++++++++++++++-----
IC(8,5,129) = +++++++++++++++++++++++++++++++++++++++++++++++++++-+---
IC(8,5,130) = +++++++++++++++++++++++++++++++++++++++++++++++++++-++--
IC(8,5,131) = ++++++++++++++++++++++++++++++++++++++++++++++++++++----
IC(8,5,132) = +++++++++++++++++++++++++++++++++++++++++++++++++++++---
IC(8,5,133) = ++++++++++++++++++++++++++++++++++++++++++++++++++++++--
IC(8,5,134) = +++++++++++++++++++++++++++++++++++++++++++++++++++++++-
IC(8,5,135) = ++++++++++++++++++++++++++++++++++++++++++++++++++++++++