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):

  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 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)

RevLex-Index from to        

List of representatives of IC(7,3) stopping with c = 143: 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+++++++++++++++



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