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 = 5 (dimension = 4)

RevLex-Index from to        

List of representatives of IC(7,5) stopping with c = 25: 111112111121112112123 222233222332233233444 333444334443444555555 445555455556666666666 566666777777777777777 IC(7,5, 1) = +++++++++++++++++++++ IC(7,5, 2) = 0++++++++++++++++++++ IC(7,5, 3) = 0++++++++++0++-++-+-- IC(7,5, 4) = 0++++++++++0+++++++++ IC(7,5, 5) = 0++++++++++0++++++0++ IC(7,5, 6) = 00++++0++++++++++++++ IC(7,5, 7) = 00++++0++++++++0+-+-- IC(7,5, 8) = 00++++0++++++++0+++++ IC(7,5, 9) = 00++++0++++++++0++++0 IC(7,5,10) = 00++++0++++++++00+0++ IC(7,5,11) = 000+++00+++0+++++++++ IC(7,5,12) = 000+++00+++0++++++0++ IC(7,5,13) = 000+++00+++0++++++000 IC(7,5,14) = 000000+++++++++++++++ IC(7,5,15) = 0000000++++++++++++++ IC(7,5,16) = 0000000++++++++0+-+-- IC(7,5,17) = 0000000++++++++0+++++ IC(7,5,18) = 0000000++++++++0++++0 IC(7,5,19) = 00000000+++0+++++++++ IC(7,5,20) = 00000000+++0++++++0++ IC(7,5,21) = 00000000+++0++++++000 IC(7,5,22) = 00000000000++++++++++ IC(7,5,23) = 000000000000+++++++++ IC(7,5,24) = 000000000000++++++0++ IC(7,5,25) = 000000000000000++++++



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