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 = 4 (dimension = 3)

RevLex-Index from to        

List of representatives of IC(7,4) stopping with c = 206: 11112111211212311121121231121231234 22233223323344422332334442334445555 33444344455555534445555556666666666 45555666666666677777777777777777777 IC(7,4, 1) = ++++++++++++++++++++++++-++++------ IC(7,4, 2) = +++++++++++++++++++++++++++-------+ IC(7,4, 3) = ++++++++++++++++++++++++++++--+--++ IC(7,4, 4) = ++++++++++++++++++++++++++++-++---+ IC(7,4, 5) = ++++++++++++++++++++++++++++-++--++ IC(7,4, 6) = ++++++++++++++++++++++++++++++----- IC(7,4, 7) = ++++++++++++++++++++++++++++++-+--- IC(7,4, 8) = ++++++++++++++++++++++++++++++++--- IC(7,4, 9) = +++++++++++++++++++++++++++++++++-- IC(7,4, 10) = ++++++++++++++++++++++++++++++++++- IC(7,4, 11) = +++++++++++++++++++++++++++++++++++ IC(7,4, 12) = 0+++++++++++++++++++++-+++-+--+--++ IC(7,4, 13) = 0++++++++++++++++++++++-----+--+--- IC(7,4, 14) = 0++++++++++++++++++++++---+-+--+--- IC(7,4, 15) = 0++++++++++++++++++++++--++-------- IC(7,4, 16) = 0+++++++++++++++++++++++-+--------- IC(7,4, 17) = 0+++++++++++++++++++++++-++-------- IC(7,4, 18) = 0+++++++++++++++++++++++-++-+------ IC(7,4, 19) = 0+++++++++++++++++++++++-++-+--+--- IC(7,4, 20) = 0+++++++++++++++++++++++-+++------- IC(7,4, 21) = 0+++++++++++++++++++++++-++++------ IC(7,4, 22) = 0+++++++++++++++++++++++-++++--+--- IC(7,4, 23) = 0+++++++++++++++++++++++-++++--0--- IC(7,4, 24) = 0+++++++++++++++++++++++++----+--++ IC(7,4, 25) = 0+++++++++++++++++++++++++-+--+--++ IC(7,4, 26) = 0+++++++++++++++++++++++++++------- IC(7,4, 27) = 0+++++++++++++++++++++++++++------+ IC(7,4, 28) = 0+++++++++++++++++++++++++++--+---+ IC(7,4, 29) = 0+++++++++++++++++++++++++++--+--++ IC(7,4, 30) = 0+++++++++++++++++++++++++++--+--0+ IC(7,4, 31) = 0+++++++++++++++++++++++++++-++--++ IC(7,4, 32) = 0+++++++++++++++++++++++++++-++-+++ IC(7,4, 33) = 0+++++++++++++++++++++++++++-++-0++ IC(7,4, 34) = 0++++++++++++++++++++++++++++------ IC(7,4, 35) = 0++++++++++++++++++++++++++++--+--- IC(7,4, 36) = 0+++++++++++++++++++++++++++++----- IC(7,4, 37) = 0+++++++++++++++++++++++++++++-+--- IC(7,4, 38) = 0+++++++++++++++++++++++++++++-++-- IC(7,4, 39) = 0+++++++++++++++++++++++++++++-+0-- IC(7,4, 40) = 0+++++++++++++++++++++++++++++-0--- IC(7,4, 41) = 0++++++++++++++++++++++++++++++++-- IC(7,4, 42) = 0+++++++++++++++++++++++++++++++++- IC(7,4, 43) = 0++++++++++++++++++++++++++++++++++ IC(7,4, 44) = 0+++++++++++++++++++++++++++++++0-- IC(7,4, 45) = 0++++++++++++++++++++++++++++++0+++ IC(7,4, 46) = 0++++++++0+-+--+++++++---+++--+-++- IC(7,4, 47) = 0++++++++0+-+--+++++++--++++--+-++- IC(7,4, 48) = 0++++++++0+-+--++++++++--+-+--+-++- IC(7,4, 49) = 0++++++++0+-+--++++++++--+++----++- IC(7,4, 50) = 0++++++++0+-+--++++++++--+++--+-++- IC(7,4, 51) = 0++++++++0+-+--++++++++--+++--0-++- IC(7,4, 52) = 0++++++++0+-+--++++++++--+++-++-++- IC(7,4, 53) = 0++++++++0+-+--++++++++--+++-++-+++ IC(7,4, 54) = 0++++++++0+-+--++++++++--+++-++-++0 IC(7,4, 55) = 0++++++++0+-+--+++++++++-+-+-++-+++ IC(7,4, 56) = 0++++++++0+-+--+++++++++-+++-++-+++ IC(7,4, 57) = 0++++++++0+-+--+++++++++-++++++-+++ IC(7,4, 58) = 0++++++++0+-+--+++++++++++-+-++-+++ IC(7,4, 59) = 0++++++++0+-+--+++++++++++++-++-+++ IC(7,4, 60) = 0++++++++0+-+--++++++++++++++++-+++ IC(7,4, 61) = 0++++++++0+-+--+++++++0+++++-++-+++ IC(7,4, 62) = 0++++++++0+++++++++++-+--++-+------ IC(7,4, 63) = 0++++++++0++++++++++++-++++-------+ IC(7,4, 64) = 0++++++++0+++++++++++++--++-------- IC(7,4, 65) = 0++++++++0+++++++++++++--++-+------ IC(7,4, 66) = 0++++++++0++++++++++++++-++-------- IC(7,4, 67) = 0++++++++0++++++++++++++-++-+------ IC(7,4, 68) = 0++++++++0++++++++++++++++--------+ IC(7,4, 69) = 0++++++++0++++++++++++++++-------++ IC(7,4, 70) = 0++++++++0++++++++++++++++-------0+ IC(7,4, 71) = 0++++++++0++++++++++++++++----+--++ IC(7,4, 72) = 0++++++++0++++++++++++++++-+--+--++ IC(7,4, 73) = 0++++++++0++++++++++++++++-+-++--++ IC(7,4, 74) = 0++++++++0+++++++++++++++++-------- IC(7,4, 75) = 0++++++++0+++++++++++++++++-------+ IC(7,4, 76) = 0++++++++0+++++++++++++++++-------0 IC(7,4, 77) = 0++++++++0+++++++++++++++++-+------ IC(7,4, 78) = 0++++++++0++++++++++++++++++------+ IC(7,4, 79) = 0++++++++0++++++++++++++++++--+---+ IC(7,4, 80) = 0++++++++0++++++++++++++++++--+--++ IC(7,4, 81) = 0++++++++0++++++++++++++++++--0---+ IC(7,4, 82) = 0++++++++0++++++++++++++++++-++--++ IC(7,4, 83) = 0++++++++0+++++++++++++++++++------ IC(7,4, 84) = 0++++++++0+++++++++++++++++++++---- IC(7,4, 85) = 0++++++++0+++++++++++++++++++++---+ IC(7,4, 86) = 0++++++++0+++++++++++++++++++++--++ IC(7,4, 87) = 0++++++++0++++++++++++++++++++0---- IC(7,4, 88) = 0++++++++0++++++++++++++0+++------- IC(7,4, 89) = 0++++++++0++++++++++++++0++++------ IC(7,4, 90) = 0++++++++0++++++++++++++0+++++----- IC(7,4, 91) = 0++++++++0+++++++++++++0-++++------ IC(7,4, 92) = 0++++++++0++++++++++++0+++-+-++--++ IC(7,4, 93) = 0++++++++0++++++++++++0++++-------+ IC(7,4, 94) = 0++++++++0++++++++++++0+++++------+ IC(7,4, 95) = 0++++++++0++++++++++++0+++++--+---+ IC(7,4, 96) = 0++++++++0++++++++++++0+++++--+--++ IC(7,4, 97) = 0++++++++0++++++++++++0+++++-++---+ IC(7,4, 98) = 0++++++++0++++++++++++0+++++-++--++ IC(7,4, 99) = 0++++++++0++++++++++++0+++++-++--0+ IC(7,4,100) = 0++++++++0++++++++++++0++++0------+ IC(7,4,101) = 0++++++++0++++++++++++0+++0-------+ IC(7,4,102) = 0++++++++0++++++++++++0+++0+-++--++ IC(7,4,103) = 0++++++++0++++++++++0----+--------- IC(7,4,104) = 0++++++++0++++++++++0----+--------+ IC(7,4,105) = 0++++++++0++++++++++0----+--------0 IC(7,4,106) = 0++++++++0++++++++++0+--++-+--+--++ IC(7,4,107) = 0++++++++0++++++++++0+-+++-+--+--++ IC(7,4,108) = 0++++++++0++++++++++0+-+++-+-++--++ IC(7,4,109) = 0++++++++0++++++++++0+-+++-+-0+--++ IC(7,4,110) = 0++++++++0++++0++++++++--++-------- IC(7,4,111) = 0++++++++0++++0+++++++++++----+--++ IC(7,4,112) = 0++++++++0++++0+++++++++++-+--+--++ IC(7,4,113) = 0++++++++0++++0+++++++++++++--+--++ IC(7,4,114) = 0++++++++0++++0+++++++++++++-++--++ IC(7,4,115) = 0++++++++0++++0++++++++++++++++--++ IC(7,4,116) = 0++++++++0++++0+++++0----+--------- IC(7,4,117) = 0++++++++0++++0+++++0+--++----+--++ IC(7,4,118) = 0++++++++0++++0+++++0+-+++----+--++ IC(7,4,119) = 0++++++++0++++0+++++0+-+++-+--+--++ IC(7,4,120) = 0++++++++0++++0+++++0+-+++-+-++--++ IC(7,4,121) = 0++++++++0++++0+++++0+-+++-+-0+--++ IC(7,4,122) = 0++++++++0++++0+++++0+-0++-+--+--++ IC(7,4,123) = 0++++++++0++++0+++++0+-0++-0--+--++ IC(7,4,124) = 00+++0+++++++++0++++++++++++++-+--- IC(7,4,125) = 00+++0+++++++++0++++++++++++++-++-- IC(7,4,126) = 00+++0+++++++++0+++++++++++++++++-- IC(7,4,127) = 00+++0+++++++++0+++++++++++++++++++ IC(7,4,128) = 00+++0+++++++++0++++++++++++++++++0 IC(7,4,129) = 00+++0++++++0++0++++++++-+++++-++-- IC(7,4,130) = 00+++0++++++0++0++++++++++++++-+--- IC(7,4,131) = 00+++0++++++0++0++++++++++++++-++-- IC(7,4,132) = 00+++0++++++0++0++++++++++++++++--- IC(7,4,133) = 00+++0++++++0++0+++++++++++++++++-- IC(7,4,134) = 00+++0++++++0++0++++++++++++++++++- IC(7,4,135) = 00+++0++++++0++0+++++++++++++0-+--- IC(7,4,136) = 00+++0++++++0++0++++++++0+++++-+--- IC(7,4,137) = 00+++0++++++0++0++++++++0+++++-++-- IC(7,4,138) = 00+++0++++++0++0++++++++0++++0-+--- IC(7,4,139) = 00+++0++++++0++0+++++++0-++++--+--- IC(7,4,140) = 00+++0++++++0000++++++++++++++++++0 IC(7,4,141) = 00000+++++++++++++++++++++++-++--++ IC(7,4,142) = 00000++++++++++++++++++++++++++--++ IC(7,4,143) = 00000++++++++++++++++++++++++++-+++ IC(7,4,144) = 00000++++++++++++++++++++++++++++-- IC(7,4,145) = 00000+++++++++++++++++++++++++++++- IC(7,4,146) = 00000++++++++++++++++++++++++++++++ IC(7,4,147) = 00000+++++++++++++++++++++0-------+ IC(7,4,148) = 00000+++++++++++++++++++++0+-++--++ IC(7,4,149) = 00000+++++++++++++++++++++0+-++-+++ IC(7,4,150) = 00000+++++++++++++++++++++0+-0+--++ IC(7,4,151) = 00000++++++++++++++++++++0+-+--+--- IC(7,4,152) = 00000++++++++++++++++++++0++++++++- IC(7,4,153) = 00000++++++++++++++++++++0+++++++++ IC(7,4,154) = 00000++++++++++++++++++++0+++++++0- IC(7,4,155) = 00000++++++++++++++++++++0++++0++-- IC(7,4,156) = 00000++++++++++++++++++++00+0++0+++ IC(7,4,157) = 000000+++++++++0++++++++++++++-+--- IC(7,4,158) = 000000+++++++++0++++++++++++++-++-- IC(7,4,159) = 000000+++++++++0+++++++++++++++---+ IC(7,4,160) = 000000+++++++++0+++++++++++++++---0 IC(7,4,161) = 000000+++++++++0++++++++++++++++--- IC(7,4,162) = 000000+++++++++0+++++++++++++++++-- IC(7,4,163) = 000000+++++++++0+++++++++++++++++++ IC(7,4,164) = 000000+++++++++0++++++++++++++++++0 IC(7,4,165) = 000000+++++++++0+++++++++++++0----- IC(7,4,166) = 000000+++++++++0+++++++++++++0-+--- IC(7,4,167) = 000000+++++++++0++++++++++++0------ IC(7,4,168) = 000000+++++++++0++++++++++++0++---+ IC(7,4,169) = 000000+++++++++0++++++++++++0++--++ IC(7,4,170) = 000000+++++++++0++++++++++++0++--0+ IC(7,4,171) = 000000+++++++++0++++++++++++0++-+++ IC(7,4,172) = 000000+++++++++0++++++++++++0++-0++ IC(7,4,173) = 000000+++++++++0++++++++++++000---0 IC(7,4,174) = 000000+++++++++0+++++++++000++-++-- IC(7,4,175) = 000000+++++++++0+++++++++000+++++++ IC(7,4,176) = 000000+++++++++0+++++++++000++++++0 IC(7,4,177) = 000000++++++0++0++++++0+++++++++--- IC(7,4,178) = 000000++++++0++0++++++0++++++++++-- IC(7,4,179) = 000000++++++0++0++++++0+++++++++++- IC(7,4,180) = 000000++++++0++0++++++0+++++++0++-- IC(7,4,181) = 000000++++++0++0++++++0+++++++0+0-- IC(7,4,182) = 000000++++++0++0++++++0++++++0-+--- IC(7,4,183) = 000000++++++0++0++++++0++000++-++-- IC(7,4,184) = 000000++++++0++0++++++0++000++++++- IC(7,4,185) = 000000++++++0++0++++++0++000+0-+0-- IC(7,4,186) = 000000++++++0++0++++++0++0000++0++0 IC(7,4,187) = 000000000++++++0000++++++++++++++++ IC(7,4,188) = 000000000++++++0000++++++++++++0+++ IC(7,4,189) = 000000000++++++0000++++++++++++0000 IC(7,4,190) = 000000000000000+++++++++++++-++--++ IC(7,4,191) = 000000000000000++++++++++++++++++-- IC(7,4,192) = 000000000000000+++++++++++++++++++- IC(7,4,193) = 000000000000000++++++++++++++++++++ IC(7,4,194) = 0000000000000000++++++++++++++-+--- IC(7,4,195) = 0000000000000000+++++++++++++++++-- IC(7,4,196) = 0000000000000000+++++++++++++++++++ IC(7,4,197) = 0000000000000000++++++++++++++++++0 IC(7,4,198) = 0000000000000000++++++0+++++++++--- IC(7,4,199) = 0000000000000000++++++0++++++++++-- IC(7,4,200) = 0000000000000000++++++0+++++++++++- IC(7,4,201) = 0000000000000000++++++0+++++++0++-- IC(7,4,202) = 0000000000000000++++++0+++++++0+0-- IC(7,4,203) = 0000000000000000++++++0++++++0-+--- IC(7,4,204) = 0000000000000000000++++++++++++++++ IC(7,4,205) = 0000000000000000000++++++++++++0+++ IC(7,4,206) = 0000000000000000000000000++++++++++



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