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 = 9, rank = 7 (dimension = 6)

RevLex-Index from to        

List of representatives of IC(9,7) stopping with c = 91: 111111121111112111112111121112112123 222222332222233222233222332233233444 333334443333444333444334443444555555 444455554445555445555455556666666666 555666665566666566666777777777777777 667777776777777888888888888888888888 788888889999999999999999999999999999 IC(9,7, 1) = ++++++++++++++++++++++++++++++++++++ IC(9,7, 2) = 0+++++++++++++++++++++++++++++++++++ IC(9,7, 3) = 0++++++++++++++0+++--+++--++--+----+ IC(9,7, 4) = 0++++++++++++++0++++-++++-+++-++-+-- IC(9,7, 5) = 0++++++++++++++0++++-++++-0+--+----- IC(9,7, 6) = 0++++++++++++++0++++++++++++++++++++ IC(9,7, 7) = 0++++++++++++++0++++++++++0++-++-+-- IC(9,7, 8) = 0++++++++++++++0++++++++++0+++++++++ IC(9,7, 9) = 0++++++++++++++0++++++++++0++++++0++ IC(9,7,10) = 00++++++0+++++++++++++++++++++++++++ IC(9,7,11) = 00++++++0++++++++++++0++--++--+----+ IC(9,7,12) = 00++++++0++++++++++++0+++-+++-++-+-- IC(9,7,13) = 00++++++0++++++++++++0+++-+++-0+-+-- IC(9,7,14) = 00++++++0++++++++++++0++++++++++++++ IC(9,7,15) = 00++++++0++++++++++++0++++++++0----+ IC(9,7,16) = 00++++++0++++++++++++0++++++++0+-+-- IC(9,7,17) = 00++++++0++++++++++++0++++++++0+++++ IC(9,7,18) = 00++++++0++++++++++++0++++++++0++++0 IC(9,7,19) = 00++++++0++++++++++++00++-0++-++-+-- IC(9,7,20) = 00++++++0++++++++++++00++-0++-++-0-- IC(9,7,21) = 00++++++0++++++++++++00+++0+++++++++ IC(9,7,22) = 00++++++0++++++++++++00+++0++++++0++ IC(9,7,23) = 00++++++0++++++++++++00+++0++++++000 IC(9,7,24) = 000+++++00+++++0++++++++++++++++++++ IC(9,7,25) = 000+++++00+++++0++++++++++0++-++-+-- IC(9,7,26) = 000+++++00+++++0++++++++++0+++++++++ IC(9,7,27) = 000+++++00+++++0++++++++++0++++++0-- IC(9,7,28) = 000+++++00+++++0++++++++++0++++++0++ IC(9,7,29) = 000+++++00+++++0++++++++++00+-0+-+-- IC(9,7,30) = 000+++++00+++++0++++++++++00++0+++++ IC(9,7,31) = 000+++++00+++++0++++++++++00++0++++0 IC(9,7,32) = 000+++++00+++++0++++++++++000+00+0++ IC(9,7,33) = 0000++++000++++00++++0++++++++++++++ IC(9,7,34) = 0000++++000++++00++++0++++++++0+-+-- IC(9,7,35) = 0000++++000++++00++++0++++++++0+++++ IC(9,7,36) = 0000++++000++++00++++0++++++++0++++0 IC(9,7,37) = 0000++++000++++00++++0++++++++00+0++ IC(9,7,38) = 0000++++000++++00++++0++++++++000000 IC(9,7,39) = 00000+++0000+++000+++00+++0+++++++++ IC(9,7,40) = 00000+++0000+++000+++00+++0++++++0++ IC(9,7,41) = 00000+++0000+++000+++00+++0++++++000 IC(9,7,42) = 00000000++++++++++++++++++++++++++++ IC(9,7,43) = 000000000+++++++++++++++++++++++++++ IC(9,7,44) = 000000000++++++++++++0++--++--+----+ IC(9,7,45) = 000000000++++++++++++0+++-+++-++-+-- IC(9,7,46) = 000000000++++++++++++0++++++++++++++ IC(9,7,47) = 000000000++++++++++++0++++++++0+-+-- IC(9,7,48) = 000000000++++++++++++0++++++++0+++++ IC(9,7,49) = 000000000++++++++++++0++++++++0++++0 IC(9,7,50) = 0000000000+++++0++++++++++++++++++++ IC(9,7,51) = 0000000000+++++0++++++++++0++-++-+-- IC(9,7,52) = 0000000000+++++0++++++++++0+++++++++ IC(9,7,53) = 0000000000+++++0++++++++++0++++++0-- IC(9,7,54) = 0000000000+++++0++++++++++0++++++0++ IC(9,7,55) = 0000000000+++++0++++++++++00+-0+-+-- IC(9,7,56) = 0000000000+++++0++++++++++00++0+++++ IC(9,7,57) = 0000000000+++++0++++++++++00++0++++0 IC(9,7,58) = 00000000000++++00++++0++++++++++++++ IC(9,7,59) = 00000000000++++00++++0++++++++0+-+-- IC(9,7,60) = 00000000000++++00++++0++++++++0+++++ IC(9,7,61) = 00000000000++++00++++0++++++++0++++0 IC(9,7,62) = 00000000000++++00++++0++++++++00+0++ IC(9,7,63) = 00000000000++++00++++0++++++++000000 IC(9,7,64) = 000000000000+++000+++00+++0+++++++++ IC(9,7,65) = 000000000000+++000+++00+++0++++++0++ IC(9,7,66) = 000000000000+++000+++00+++0++++++000 IC(9,7,67) = 000000000000000+++++++++++++++++++++ IC(9,7,68) = 0000000000000000++++++++++++++++++++ IC(9,7,69) = 0000000000000000++++++++++0++-++-+-- IC(9,7,70) = 0000000000000000++++++++++0+++++++++ IC(9,7,71) = 0000000000000000++++++++++0++++++0++ IC(9,7,72) = 00000000000000000++++0++++++++++++++ IC(9,7,73) = 00000000000000000++++0++++++++0+-+-- IC(9,7,74) = 00000000000000000++++0++++++++0+++++ IC(9,7,75) = 00000000000000000++++0++++++++0++++0 IC(9,7,76) = 00000000000000000++++0++++++++00+0++ IC(9,7,77) = 000000000000000000+++00+++0+++++++++ IC(9,7,78) = 000000000000000000+++00+++0++++++0++ IC(9,7,79) = 000000000000000000+++00+++0++++++000 IC(9,7,80) = 000000000000000000000+++++++++++++++ IC(9,7,81) = 0000000000000000000000++++++++++++++ IC(9,7,82) = 0000000000000000000000++++++++0+-+-- IC(9,7,83) = 0000000000000000000000++++++++0+++++ IC(9,7,84) = 0000000000000000000000++++++++0++++0 IC(9,7,85) = 00000000000000000000000+++0+++++++++ IC(9,7,86) = 00000000000000000000000+++0++++++0++ IC(9,7,87) = 00000000000000000000000+++0++++++000 IC(9,7,88) = 00000000000000000000000000++++++++++ IC(9,7,89) = 000000000000000000000000000+++++++++ IC(9,7,90) = 000000000000000000000000000++++++0++ IC(9,7,91) = 000000000000000000000000000000++++++



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