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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.
381,906 matroids, showing 21,801–21,850
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.12.433007 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.433025 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.433029 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.433041 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.433043 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.433044 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.433047 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.433052 | 3 | 12 | 206 | 1 | ✓ | all | 6 | ? |
| 3.12.433057 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.433060 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.433083 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.433124 | 3 | 12 | 210 | 1 | ✓ | all | 6 | ? |
| 3.12.433125 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.433135 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.433147 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.433171 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.433177 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.433178 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.433185 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.433196 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.433198 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.433209 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.433215 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.433233 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.433240 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.433245 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.433255 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.433264 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.433269 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.433286 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.433331 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.433358 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.433395 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.433408 | 3 | 12 | 206 | 1 | ✓ | all | 6 | ? |
| 3.12.433417 | 3 | 12 | 206 | 1 | ✓ | all | 6 | ? |
| 3.12.433433 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.433443 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.433449 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.433460 | 3 | 12 | 206 | 1 | ✓ | all | 6 | ? |
| 3.12.433471 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.433473 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.433474 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.433483 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.433485 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.433494 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.433513 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.433519 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.433524 | 3 | 12 | 206 | 1 | ✓ | all | 6 | ? |
| 3.12.433532 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.433550 | 3 | 12 | 206 | 1 | ✓ | all | 6 | ? |