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+++