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):

  All   Non-degenerate (Uniform)
  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)

RevLex-Index from to        

List of non-degenerate representatives of IC(8,3) stopping with c = 135: 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) = ++++++++++++++++++++++++++++++++++++++++++++++++++++++++



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