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 = 6, rank = 4 (dimension = 3)

RevLex-Index from to        

List of representatives of IC(6,4) stopping with c = 12: 111121112112123 222332233233444 334443444555555 455556666666666 IC(6,4, 1) = +++++++++++++++ IC(6,4, 2) = 0++++++++++++++ IC(6,4, 3) = 0++++++++0+-+-- IC(6,4, 4) = 0++++++++0+++++ IC(6,4, 5) = 0++++++++0++++0 IC(6,4, 6) = 00+++0+++++++++ IC(6,4, 7) = 00+++0++++++0++ IC(6,4, 8) = 00+++0++++++000 IC(6,4, 9) = 00000++++++++++ IC(6,4,10) = 000000+++++++++ IC(6,4,11) = 000000++++++0++ IC(6,4,12) = 000000000++++++



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