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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 22,601–22,650
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.12.450619 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.450645 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.450649 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.450737 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.450769 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.450829 | 3 | 12 | 206 | 1 | ✓ | all | 6 | ? |
| 3.12.450856 | 3 | 12 | 206 | 1 | ✓ | all | 6 | ? |
| 3.12.450873 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.450941 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.450952 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.450980 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.450989 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.451015 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.451017 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.451039 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.451064 | 3 | 12 | 206 | 1 | ✓ | all | 6 | ? |
| 3.12.451093 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.451100 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.451108 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.451132 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.451140 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.451208 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.451225 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.451236 | 3 | 12 | 207 | 2 | ✓ | all | 6 | ? |
| 3.12.451267 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.451277 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.451289 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.451299 | 3 | 12 | 206 | 1 | ✓ | all | 6 | ? |
| 3.12.451303 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.451313 | 3 | 12 | 206 | 1 | ✓ | all | 6 | ? |
| 3.12.451386 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.451390 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.451479 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.451491 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.451492 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.451511 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.451522 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.451534 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.451557 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.451563 | 3 | 12 | 206 | 1 | ✓ | all | 6 | ? |
| 3.12.451566 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.451570 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.451575 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.451579 | 3 | 12 | 206 | 1 | ✓ | all | 6 | ? |
| 3.12.451599 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.451613 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.451677 | 3 | 12 | 211 | 4 | ✓ | all | 6 | ? |
| 3.12.451700 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.451702 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.451717 | 3 | 12 | 210 | 2 | ✓ | all | 6 | ? |