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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 22,351–22,400
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.12.444510 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.444511 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.444523 | 3 | 12 | 206 | 1 | ✓ | all | 6 | ? |
| 3.12.444555 | 3 | 12 | 206 | 1 | ✓ | all | 6 | ? |
| 3.12.444556 | 3 | 12 | 206 | 1 | ✓ | all | 6 | ? |
| 3.12.444568 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.444582 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.444586 | 3 | 12 | 206 | 1 | ✓ | all | 6 | ? |
| 3.12.444590 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.444604 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.444621 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.444655 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.444667 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.444691 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.444722 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.444792 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.444860 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.445010 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.445032 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.445072 | 3 | 12 | 206 | 1 | ✓ | all | 6 | ? |
| 3.12.445080 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.445081 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.445098 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.445102 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.445112 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.445115 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.445167 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.445181 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.445184 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.445267 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.445277 | 3 | 12 | 210 | 1 | ✓ | all | 6 | ? |
| 3.12.445328 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.445372 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.445471 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.445679 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.445741 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.445757 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.445766 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.445787 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.445911 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.445950 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.445969 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.445992 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.445998 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.446085 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.446093 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.446147 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.446211 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.446236 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.446314 | 3 | 12 | 206 | 1 | ✓ | all | 6 | ? |