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 = 8, rank = 6 (dimension = 5)

RevLex-Index from to        

List of representatives of IC(8,6) stopping with c = 50: 1111112111112111121112112123 2222233222233222332233233444 3333444333444334443444555555 4445555445555455556666666666 5566666566666777777777777777 6777777888888888888888888888 IC(8,6, 1) = ++++++++++++++++++++++++++++ IC(8,6, 2) = 0+++++++++++++++++++++++++++ IC(8,6, 3) = 0++++++++++++0++--++--+----+ IC(8,6, 4) = 0++++++++++++0+++-+++-++-+-- IC(8,6, 5) = 0++++++++++++0++++++++++++++ IC(8,6, 6) = 0++++++++++++0++++++++0+-+-- IC(8,6, 7) = 0++++++++++++0++++++++0+++++ IC(8,6, 8) = 0++++++++++++0++++++++0++++0 IC(8,6, 9) = 00+++++0++++++++++++++++++++ IC(8,6,10) = 00+++++0++++++++++0++-++-+-- IC(8,6,11) = 00+++++0++++++++++0+++++++++ IC(8,6,12) = 00+++++0++++++++++0++++++0-- IC(8,6,13) = 00+++++0++++++++++0++++++0++ IC(8,6,14) = 00+++++0++++++++++00+-0+-+-- IC(8,6,15) = 00+++++0++++++++++00++0+++++ IC(8,6,16) = 00+++++0++++++++++00++0++++0 IC(8,6,17) = 000++++00++++0++++++++++++++ IC(8,6,18) = 000++++00++++0++++++++0+-+-- IC(8,6,19) = 000++++00++++0++++++++0+++++ IC(8,6,20) = 000++++00++++0++++++++0++++0 IC(8,6,21) = 000++++00++++0++++++++00+0++ IC(8,6,22) = 000++++00++++0++++++++000000 IC(8,6,23) = 0000+++000+++00+++0+++++++++ IC(8,6,24) = 0000+++000+++00+++0++++++0++ IC(8,6,25) = 0000+++000+++00+++0++++++000 IC(8,6,26) = 0000000+++++++++++++++++++++ IC(8,6,27) = 00000000++++++++++++++++++++ IC(8,6,28) = 00000000++++++++++0++-++-+-- IC(8,6,29) = 00000000++++++++++0+++++++++ IC(8,6,30) = 00000000++++++++++0++++++0++ IC(8,6,31) = 000000000++++0++++++++++++++ IC(8,6,32) = 000000000++++0++++++++0+-+-- IC(8,6,33) = 000000000++++0++++++++0+++++ IC(8,6,34) = 000000000++++0++++++++0++++0 IC(8,6,35) = 000000000++++0++++++++00+0++ IC(8,6,36) = 0000000000+++00+++0+++++++++ IC(8,6,37) = 0000000000+++00+++0++++++0++ IC(8,6,38) = 0000000000+++00+++0++++++000 IC(8,6,39) = 0000000000000+++++++++++++++ IC(8,6,40) = 00000000000000++++++++++++++ IC(8,6,41) = 00000000000000++++++++0+-+-- IC(8,6,42) = 00000000000000++++++++0+++++ IC(8,6,43) = 00000000000000++++++++0++++0 IC(8,6,44) = 000000000000000+++0+++++++++ IC(8,6,45) = 000000000000000+++0++++++0++ IC(8,6,46) = 000000000000000+++0++++++000 IC(8,6,47) = 000000000000000000++++++++++ IC(8,6,48) = 0000000000000000000+++++++++ IC(8,6,49) = 0000000000000000000++++++0++ IC(8,6,50) = 0000000000000000000000++++++



Maintained by Lukas Finschi (finschi [at] ifor.math.ethz.ch)