Catalog of Isomorphism Classes of Oriented Matroids

The following table shows the number of non-degenerate (uniform) 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 1 1 4 11 135 4 382 312 356
rank = 4 (dim = 3) 1 1 1 11 2 628 9 276 595 unknown
rank = 5 (dim = 4) 1 1 1 135 9 276 595 unknown
rank = 6 (dim = 5) 1 1 1 4 382 unknown
rank = 7 (dim = 6) 1 1 1 312 356
rank = 8 (dim = 7) 1 1 1
rank = 9 (dim = 8) 1 1
rank = 10 (dim = 9) 1

Cardinality = 7, rank = 4 (dimension = 3)

RevLex-Index from to        

List of non-degenerate representatives of IC(7,4) stopping with c = 11: 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) = +++++++++++++++++++++++++++++++++++



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