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 = 5 (dimension = 4)

RevLex-Index from to        

List of non-degenerate representatives of IC(8,5) stopping with c = 135: 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) = ++++++++++++++++++++++++++++++++++++++++++++++++++++++++



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