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 = 10, rank = 9 (dimension = 8)

RevLex-Index from to        

List of representatives of IC(10,9) stopping with c = 8: 1111111112 2222222233 3333333444 4444445555 5555566666 6666777777 7778888888 8899999999 9aaaaaaaaa IC(10,9,1) = ++++++++++ IC(10,9,2) = 0+++++++++ IC(10,9,3) = 00++++++++ IC(10,9,4) = 000+++++++ IC(10,9,5) = 0000++++++ IC(10,9,6) = 00000+++++ IC(10,9,7) = 000000++++ IC(10,9,8) = 0000000+++



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