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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 21,951–22,000
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.12.436149 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.436177 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.436235 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.436276 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.436329 | 3 | 12 | 210 | 1 | ✓ | all | 6 | ? |
| 3.12.436543 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.436558 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.436593 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.436598 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.436622 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.436642 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.436664 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.436698 | 3 | 12 | 210 | 1 | ✓ | all | 6 | ? |
| 3.12.436700 | 3 | 12 | 210 | 1 | ✓ | all | 6 | ? |
| 3.12.436711 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.436739 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.436751 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.436775 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.436787 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.436829 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.436838 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.436861 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.436882 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.436925 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.436938 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.436983 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.436985 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.437011 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.437034 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.437065 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.437077 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.437101 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.437145 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.437153 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.437179 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.437190 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.437206 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.437216 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.437277 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.437294 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.437335 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.437416 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.437429 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.437454 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.437744 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.437751 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.437772 | 3 | 12 | 209 | 2 | ✓ | all | 6 | ? |
| 3.12.437778 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.437783 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.437797 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |