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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):
|
|
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 = 7, rank = 4 (dimension = 3)
List of the 206 representatives of IC(7,4), ordered by the RevLex-Index.
The numbers above the signs indicate the elements of the corresponding basis.
11112111211212311121121231121231234
22233223323344422332334442334445555
33444344455555534445555556666666666
45555666666666677777777777777777777
IC(7,4, 1) = ++++++++++++++++++++++++-++++------
IC(7,4, 2) = +++++++++++++++++++++++++++-------+
IC(7,4, 3) = ++++++++++++++++++++++++++++--+--++
IC(7,4, 4) = ++++++++++++++++++++++++++++-++---+
IC(7,4, 5) = ++++++++++++++++++++++++++++-++--++
IC(7,4, 6) = ++++++++++++++++++++++++++++++-----
IC(7,4, 7) = ++++++++++++++++++++++++++++++-+---
IC(7,4, 8) = ++++++++++++++++++++++++++++++++---
IC(7,4, 9) = +++++++++++++++++++++++++++++++++--
IC(7,4, 10) = ++++++++++++++++++++++++++++++++++-
IC(7,4, 11) = +++++++++++++++++++++++++++++++++++
IC(7,4, 12) = 0+++++++++++++++++++++-+++-+--+--++
IC(7,4, 13) = 0++++++++++++++++++++++-----+--+---
IC(7,4, 14) = 0++++++++++++++++++++++---+-+--+---
IC(7,4, 15) = 0++++++++++++++++++++++--++--------
IC(7,4, 16) = 0+++++++++++++++++++++++-+---------
IC(7,4, 17) = 0+++++++++++++++++++++++-++--------
IC(7,4, 18) = 0+++++++++++++++++++++++-++-+------
IC(7,4, 19) = 0+++++++++++++++++++++++-++-+--+---
IC(7,4, 20) = 0+++++++++++++++++++++++-+++-------
IC(7,4, 21) = 0+++++++++++++++++++++++-++++------
IC(7,4, 22) = 0+++++++++++++++++++++++-++++--+---
IC(7,4, 23) = 0+++++++++++++++++++++++-++++--0---
IC(7,4, 24) = 0+++++++++++++++++++++++++----+--++
IC(7,4, 25) = 0+++++++++++++++++++++++++-+--+--++
IC(7,4, 26) = 0+++++++++++++++++++++++++++-------
IC(7,4, 27) = 0+++++++++++++++++++++++++++------+
IC(7,4, 28) = 0+++++++++++++++++++++++++++--+---+
IC(7,4, 29) = 0+++++++++++++++++++++++++++--+--++
IC(7,4, 30) = 0+++++++++++++++++++++++++++--+--0+
IC(7,4, 31) = 0+++++++++++++++++++++++++++-++--++
IC(7,4, 32) = 0+++++++++++++++++++++++++++-++-+++
IC(7,4, 33) = 0+++++++++++++++++++++++++++-++-0++
IC(7,4, 34) = 0++++++++++++++++++++++++++++------
IC(7,4, 35) = 0++++++++++++++++++++++++++++--+---
IC(7,4, 36) = 0+++++++++++++++++++++++++++++-----
IC(7,4, 37) = 0+++++++++++++++++++++++++++++-+---
IC(7,4, 38) = 0+++++++++++++++++++++++++++++-++--
IC(7,4, 39) = 0+++++++++++++++++++++++++++++-+0--
IC(7,4, 40) = 0+++++++++++++++++++++++++++++-0---
IC(7,4, 41) = 0++++++++++++++++++++++++++++++++--
IC(7,4, 42) = 0+++++++++++++++++++++++++++++++++-
IC(7,4, 43) = 0++++++++++++++++++++++++++++++++++
IC(7,4, 44) = 0+++++++++++++++++++++++++++++++0--
IC(7,4, 45) = 0++++++++++++++++++++++++++++++0+++
IC(7,4, 46) = 0++++++++0+-+--+++++++---+++--+-++-
IC(7,4, 47) = 0++++++++0+-+--+++++++--++++--+-++-
IC(7,4, 48) = 0++++++++0+-+--++++++++--+-+--+-++-
IC(7,4, 49) = 0++++++++0+-+--++++++++--+++----++-
IC(7,4, 50) = 0++++++++0+-+--++++++++--+++--+-++-
IC(7,4, 51) = 0++++++++0+-+--++++++++--+++--0-++-
IC(7,4, 52) = 0++++++++0+-+--++++++++--+++-++-++-
IC(7,4, 53) = 0++++++++0+-+--++++++++--+++-++-+++
IC(7,4, 54) = 0++++++++0+-+--++++++++--+++-++-++0
IC(7,4, 55) = 0++++++++0+-+--+++++++++-+-+-++-+++
IC(7,4, 56) = 0++++++++0+-+--+++++++++-+++-++-+++
IC(7,4, 57) = 0++++++++0+-+--+++++++++-++++++-+++
IC(7,4, 58) = 0++++++++0+-+--+++++++++++-+-++-+++
IC(7,4, 59) = 0++++++++0+-+--+++++++++++++-++-+++
IC(7,4, 60) = 0++++++++0+-+--++++++++++++++++-+++
IC(7,4, 61) = 0++++++++0+-+--+++++++0+++++-++-+++
IC(7,4, 62) = 0++++++++0+++++++++++-+--++-+------
IC(7,4, 63) = 0++++++++0++++++++++++-++++-------+
IC(7,4, 64) = 0++++++++0+++++++++++++--++--------
IC(7,4, 65) = 0++++++++0+++++++++++++--++-+------
IC(7,4, 66) = 0++++++++0++++++++++++++-++--------
IC(7,4, 67) = 0++++++++0++++++++++++++-++-+------
IC(7,4, 68) = 0++++++++0++++++++++++++++--------+
IC(7,4, 69) = 0++++++++0++++++++++++++++-------++
IC(7,4, 70) = 0++++++++0++++++++++++++++-------0+
IC(7,4, 71) = 0++++++++0++++++++++++++++----+--++
IC(7,4, 72) = 0++++++++0++++++++++++++++-+--+--++
IC(7,4, 73) = 0++++++++0++++++++++++++++-+-++--++
IC(7,4, 74) = 0++++++++0+++++++++++++++++--------
IC(7,4, 75) = 0++++++++0+++++++++++++++++-------+
IC(7,4, 76) = 0++++++++0+++++++++++++++++-------0
IC(7,4, 77) = 0++++++++0+++++++++++++++++-+------
IC(7,4, 78) = 0++++++++0++++++++++++++++++------+
IC(7,4, 79) = 0++++++++0++++++++++++++++++--+---+
IC(7,4, 80) = 0++++++++0++++++++++++++++++--+--++
IC(7,4, 81) = 0++++++++0++++++++++++++++++--0---+
IC(7,4, 82) = 0++++++++0++++++++++++++++++-++--++
IC(7,4, 83) = 0++++++++0+++++++++++++++++++------
IC(7,4, 84) = 0++++++++0+++++++++++++++++++++----
IC(7,4, 85) = 0++++++++0+++++++++++++++++++++---+
IC(7,4, 86) = 0++++++++0+++++++++++++++++++++--++
IC(7,4, 87) = 0++++++++0++++++++++++++++++++0----
IC(7,4, 88) = 0++++++++0++++++++++++++0+++-------
IC(7,4, 89) = 0++++++++0++++++++++++++0++++------
IC(7,4, 90) = 0++++++++0++++++++++++++0+++++-----
IC(7,4, 91) = 0++++++++0+++++++++++++0-++++------
IC(7,4, 92) = 0++++++++0++++++++++++0+++-+-++--++
IC(7,4, 93) = 0++++++++0++++++++++++0++++-------+
IC(7,4, 94) = 0++++++++0++++++++++++0+++++------+
IC(7,4, 95) = 0++++++++0++++++++++++0+++++--+---+
IC(7,4, 96) = 0++++++++0++++++++++++0+++++--+--++
IC(7,4, 97) = 0++++++++0++++++++++++0+++++-++---+
IC(7,4, 98) = 0++++++++0++++++++++++0+++++-++--++
IC(7,4, 99) = 0++++++++0++++++++++++0+++++-++--0+
IC(7,4,100) = 0++++++++0++++++++++++0++++0------+
IC(7,4,101) = 0++++++++0++++++++++++0+++0-------+
IC(7,4,102) = 0++++++++0++++++++++++0+++0+-++--++
IC(7,4,103) = 0++++++++0++++++++++0----+---------
IC(7,4,104) = 0++++++++0++++++++++0----+--------+
IC(7,4,105) = 0++++++++0++++++++++0----+--------0
IC(7,4,106) = 0++++++++0++++++++++0+--++-+--+--++
IC(7,4,107) = 0++++++++0++++++++++0+-+++-+--+--++
IC(7,4,108) = 0++++++++0++++++++++0+-+++-+-++--++
IC(7,4,109) = 0++++++++0++++++++++0+-+++-+-0+--++
IC(7,4,110) = 0++++++++0++++0++++++++--++--------
IC(7,4,111) = 0++++++++0++++0+++++++++++----+--++
IC(7,4,112) = 0++++++++0++++0+++++++++++-+--+--++
IC(7,4,113) = 0++++++++0++++0+++++++++++++--+--++
IC(7,4,114) = 0++++++++0++++0+++++++++++++-++--++
IC(7,4,115) = 0++++++++0++++0++++++++++++++++--++
IC(7,4,116) = 0++++++++0++++0+++++0----+---------
IC(7,4,117) = 0++++++++0++++0+++++0+--++----+--++
IC(7,4,118) = 0++++++++0++++0+++++0+-+++----+--++
IC(7,4,119) = 0++++++++0++++0+++++0+-+++-+--+--++
IC(7,4,120) = 0++++++++0++++0+++++0+-+++-+-++--++
IC(7,4,121) = 0++++++++0++++0+++++0+-+++-+-0+--++
IC(7,4,122) = 0++++++++0++++0+++++0+-0++-+--+--++
IC(7,4,123) = 0++++++++0++++0+++++0+-0++-0--+--++
IC(7,4,124) = 00+++0+++++++++0++++++++++++++-+---
IC(7,4,125) = 00+++0+++++++++0++++++++++++++-++--
IC(7,4,126) = 00+++0+++++++++0+++++++++++++++++--
IC(7,4,127) = 00+++0+++++++++0+++++++++++++++++++
IC(7,4,128) = 00+++0+++++++++0++++++++++++++++++0
IC(7,4,129) = 00+++0++++++0++0++++++++-+++++-++--
IC(7,4,130) = 00+++0++++++0++0++++++++++++++-+---
IC(7,4,131) = 00+++0++++++0++0++++++++++++++-++--
IC(7,4,132) = 00+++0++++++0++0++++++++++++++++---
IC(7,4,133) = 00+++0++++++0++0+++++++++++++++++--
IC(7,4,134) = 00+++0++++++0++0++++++++++++++++++-
IC(7,4,135) = 00+++0++++++0++0+++++++++++++0-+---
IC(7,4,136) = 00+++0++++++0++0++++++++0+++++-+---
IC(7,4,137) = 00+++0++++++0++0++++++++0+++++-++--
IC(7,4,138) = 00+++0++++++0++0++++++++0++++0-+---
IC(7,4,139) = 00+++0++++++0++0+++++++0-++++--+---
IC(7,4,140) = 00+++0++++++0000++++++++++++++++++0
IC(7,4,141) = 00000+++++++++++++++++++++++-++--++
IC(7,4,142) = 00000++++++++++++++++++++++++++--++
IC(7,4,143) = 00000++++++++++++++++++++++++++-+++
IC(7,4,144) = 00000++++++++++++++++++++++++++++--
IC(7,4,145) = 00000+++++++++++++++++++++++++++++-
IC(7,4,146) = 00000++++++++++++++++++++++++++++++
IC(7,4,147) = 00000+++++++++++++++++++++0-------+
IC(7,4,148) = 00000+++++++++++++++++++++0+-++--++
IC(7,4,149) = 00000+++++++++++++++++++++0+-++-+++
IC(7,4,150) = 00000+++++++++++++++++++++0+-0+--++
IC(7,4,151) = 00000++++++++++++++++++++0+-+--+---
IC(7,4,152) = 00000++++++++++++++++++++0++++++++-
IC(7,4,153) = 00000++++++++++++++++++++0+++++++++
IC(7,4,154) = 00000++++++++++++++++++++0+++++++0-
IC(7,4,155) = 00000++++++++++++++++++++0++++0++--
IC(7,4,156) = 00000++++++++++++++++++++00+0++0+++
IC(7,4,157) = 000000+++++++++0++++++++++++++-+---
IC(7,4,158) = 000000+++++++++0++++++++++++++-++--
IC(7,4,159) = 000000+++++++++0+++++++++++++++---+
IC(7,4,160) = 000000+++++++++0+++++++++++++++---0
IC(7,4,161) = 000000+++++++++0++++++++++++++++---
IC(7,4,162) = 000000+++++++++0+++++++++++++++++--
IC(7,4,163) = 000000+++++++++0+++++++++++++++++++
IC(7,4,164) = 000000+++++++++0++++++++++++++++++0
IC(7,4,165) = 000000+++++++++0+++++++++++++0-----
IC(7,4,166) = 000000+++++++++0+++++++++++++0-+---
IC(7,4,167) = 000000+++++++++0++++++++++++0------
IC(7,4,168) = 000000+++++++++0++++++++++++0++---+
IC(7,4,169) = 000000+++++++++0++++++++++++0++--++
IC(7,4,170) = 000000+++++++++0++++++++++++0++--0+
IC(7,4,171) = 000000+++++++++0++++++++++++0++-+++
IC(7,4,172) = 000000+++++++++0++++++++++++0++-0++
IC(7,4,173) = 000000+++++++++0++++++++++++000---0
IC(7,4,174) = 000000+++++++++0+++++++++000++-++--
IC(7,4,175) = 000000+++++++++0+++++++++000+++++++
IC(7,4,176) = 000000+++++++++0+++++++++000++++++0
IC(7,4,177) = 000000++++++0++0++++++0+++++++++---
IC(7,4,178) = 000000++++++0++0++++++0++++++++++--
IC(7,4,179) = 000000++++++0++0++++++0+++++++++++-
IC(7,4,180) = 000000++++++0++0++++++0+++++++0++--
IC(7,4,181) = 000000++++++0++0++++++0+++++++0+0--
IC(7,4,182) = 000000++++++0++0++++++0++++++0-+---
IC(7,4,183) = 000000++++++0++0++++++0++000++-++--
IC(7,4,184) = 000000++++++0++0++++++0++000++++++-
IC(7,4,185) = 000000++++++0++0++++++0++000+0-+0--
IC(7,4,186) = 000000++++++0++0++++++0++0000++0++0
IC(7,4,187) = 000000000++++++0000++++++++++++++++
IC(7,4,188) = 000000000++++++0000++++++++++++0+++
IC(7,4,189) = 000000000++++++0000++++++++++++0000
IC(7,4,190) = 000000000000000+++++++++++++-++--++
IC(7,4,191) = 000000000000000++++++++++++++++++--
IC(7,4,192) = 000000000000000+++++++++++++++++++-
IC(7,4,193) = 000000000000000++++++++++++++++++++
IC(7,4,194) = 0000000000000000++++++++++++++-+---
IC(7,4,195) = 0000000000000000+++++++++++++++++--
IC(7,4,196) = 0000000000000000+++++++++++++++++++
IC(7,4,197) = 0000000000000000++++++++++++++++++0
IC(7,4,198) = 0000000000000000++++++0+++++++++---
IC(7,4,199) = 0000000000000000++++++0++++++++++--
IC(7,4,200) = 0000000000000000++++++0+++++++++++-
IC(7,4,201) = 0000000000000000++++++0+++++++0++--
IC(7,4,202) = 0000000000000000++++++0+++++++0+0--
IC(7,4,203) = 0000000000000000++++++0++++++0-+---
IC(7,4,204) = 0000000000000000000++++++++++++++++
IC(7,4,205) = 0000000000000000000++++++++++++0+++
IC(7,4,206) = 0000000000000000000000000++++++++++