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 = 8, rank = 4 (dimension = 3)

List of the 2628 non-degenerate (uniform) representatives of IC(8,4), ordered by the RevLex-Index.
The numbers above the signs indicate the elements of the corresponding basis.

               1111211121121231112112123112123123411121121231121231234112123123412345
               2223322332334442233233444233444555522332334442334445555233444555566666
               3344434445555553444555555666666666634445555556666666666777777777777777
               4555566666666667777777777777777777788888888888888888888888888888888888



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