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…or describe it by its bases, non-bases or lines
Any labeling of the ground set $\{1,\dots,n\}$ will do: we compute the canonical id.
Sets are written as {1,2,3}, one per line, or, when $n \le 9$, as digit strings such as
123 145. Lines are the lines with at least three points of a simple rank-3 matroid.
A revlex encoding is a string of * and 0.
2,030,492 matroids, showing 19,801–19,850
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.12.139923 | 3 | 12 | 211 | 1 | ✓ | all | 0 | ? |
| 3.12.139929 | 3 | 12 | 211 | 1 | ✓ | all | 0 | ? |
| 3.12.139930 | 3 | 12 | 210 | 1 | ✓ | all but 2,3,5,7,23 | 0 | ? |
| 3.12.139948 | 3 | 12 | 211 | 1 | ✓ | all | 0 | ? |
| 3.12.139954 | 3 | 12 | 211 | 1 | ✓ | all | 0 | ? |
| 3.12.139963 | 3 | 12 | 210 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.139964 | 3 | 12 | 209 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.139985 | 3 | 12 | 210 | 1 | ✓ | all but 7 | 0 | ? |
| 3.12.139992 | 3 | 12 | 210 | 1 | ✓ | all but 3 | 0 | ? |
| 3.12.139996 | 3 | 12 | 210 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.140014 | 3 | 12 | 209 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.140030 | 3 | 12 | 209 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.140037 | 3 | 12 | 210 | 1 | ✓ | all | 0 | ? |
| 3.12.140041 | 3 | 12 | 210 | 1 | ✓ | all | 0 | ? |
| 3.12.140053 | 3 | 12 | 210 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.140065 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5,7,11 | 0 | ? |
| 3.12.140075 | 3 | 12 | 209 | 1 | ✓ | all but 2,11 | 0 | ? |
| 3.12.140077 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,7,11 | 0 | ? |
| 3.12.140083 | 3 | 12 | 210 | 2 | ✓ | all but 2 | 0 | ? |
| 3.12.140084 | 3 | 12 | 210 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.140085 | 3 | 12 | 209 | 1 | ✓ | all | 0 | ? |
| 3.12.140087 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.140102 | 3 | 12 | 209 | 1 | ✓ | all but 7 | 0 | ? |
| 3.12.140103 | 3 | 12 | 210 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.140106 | 3 | 12 | 210 | 1 | ✓ | all | 0 | ? |
| 3.12.140111 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.140116 | 3 | 12 | 210 | 1 | ✓ | all | 0 | ? |
| 3.12.140124 | 3 | 12 | 209 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.140130 | 3 | 12 | 209 | 1 | ✓ | all | 0 | ? |
| 3.12.140131 | 3 | 12 | 212 | 1 | ✓ | all | 0 | ? |
| 3.12.140134 | 3 | 12 | 211 | 1 | ✓ | all but 3 | 0 | ? |
| 3.12.140141 | 3 | 12 | 210 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.140143 | 3 | 12 | 210 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.140145 | 3 | 12 | 210 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.140147 | 3 | 12 | 210 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.140155 | 3 | 12 | 211 | 1 | ✓ | all | 0 | ? |
| 3.12.140157 | 3 | 12 | 210 | 1 | ✓ | all but 2,3,7 | 0 | ? |
| 3.12.140159 | 3 | 12 | 210 | 1 | ✓ | all but 2,3,5,7 | 0 | ? |
| 3.12.140170 | 3 | 12 | 210 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.140171 | 3 | 12 | 210 | 1 | ✓ | all but 7 | 0 | ? |
| 3.12.140172 | 3 | 12 | 210 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.140194 | 3 | 12 | 210 | 1 | ✓ | all | 0 | ? |
| 3.12.140197 | 3 | 12 | 210 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.140202 | 3 | 12 | 209 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.140222 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5,7,11 | 0 | ? |
| 3.12.140226 | 3 | 12 | 210 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.140232 | 3 | 12 | 210 | 1 | ✓ | all but 2,3,5,7,11,13 | 0 | ? |
| 3.12.140239 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.140240 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.140242 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |