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

Catalog of Point Configurations

The following table shows the number of abstract order types. Data can be accessed by clicking on the corresponding number (if available):

  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 3 11 93 2 121 122 508 15 296 266 unknown
rank = 4 (dim = 3) 1 5 55 5 083 10 775 236 unknown unknown
rank = 5 (dim = 4) 1 8 204 505 336 unknown unknown
rank = 6 (dim = 5) 1 11 705 unknown unknown
rank = 7 (dim = 6) 1 15 2 293 unknown
rank = 8 (dim = 7) 1 19 7 377
rank = 9 (dim = 8) 1 24
rank = 10 (dim = 9) 1

Cardinality = 10, rank = 9 (dimension = 8)

List of the 24 representatives of OT(10,9), ordered by the RevLex-Index.
The numbers above the signs indicate the elements of the corresponding basis.


Note: The representation of the abstract order type is not lexicographically maximal.



              1111111112
              2222222233
              3333333444
              4444445555
              5555566666
              6666777777
              7778888888
              8899999999
              9aaaaaaaaa
OT(10,9, 1) = +-+-+-+---
OT(10,9, 2) = +++-+---+-
OT(10,9, 3) = +-+-++----
OT(10,9, 4) = ++-+++----
OT(10,9, 5) = +++++++--+
OT(10,9, 6) = 0+-+-+-+--
OT(10,9, 7) = 0+-+-+-++-
OT(10,9, 8) = 0++--+-+++
OT(10,9, 9) = 0+------+-
OT(10,9,10) = 00+-+---+-
OT(10,9,11) = 00+-+-----
OT(10,9,12) = 00+++-++++
OT(10,9,13) = 00+----+++
OT(10,9,14) = 000+-+---+
OT(10,9,15) = 000+-+----
OT(10,9,16) = 000++---++
OT(10,9,17) = 0000+-+++-
OT(10,9,18) = 0000++-+++
OT(10,9,19) = 0000+--+++
OT(10,9,20) = 00000+---+
OT(10,9,21) = 00000++-++
OT(10,9,22) = 000000+++-
OT(10,9,23) = 000000++--
OT(10,9,24) = 0000000+++


Maintained by Dr. Lukas Finschi Terms and Conditions Privacy Policy