Home Catalog of Oriented Matroids Catalog of Point Configurations Catalog of Hyperplane Arrangements Glossary People
Home Catalog of Oriented Matroids Catalog of Point Configurations Catalog of Hyperplane Arrangements Glossary People

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 = 6, rank = 4 (dimension = 3)

RevLex-Index from to         


List of non-degenerate representatives of IC(6,4) stopping with c = 1:
            111121112112123
            222332233233444
            334443444555555
            455556666666666
IC(6,4,1) = +++++++++++++++


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