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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 22,101–22,150
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.12.440070 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.440091 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.440101 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.440116 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.440147 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.440165 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.440168 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.440170 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.440194 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.440197 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.440207 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.440215 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.440226 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.440228 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.440236 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.440240 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.440243 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.440248 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.440272 | 3 | 12 | 210 | 1 | ✓ | all | 6 | ? |
| 3.12.440275 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.440281 | 3 | 12 | 210 | 1 | ✓ | all | 6 | ? |
| 3.12.440287 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.440312 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.440323 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.440328 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.440329 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.440340 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.440344 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.440352 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.440367 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.440375 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.440389 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.440403 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.440407 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.440412 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.440426 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.440440 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.440591 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.440670 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.440747 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.440753 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.440754 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.440755 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.440758 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.440765 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.440781 | 3 | 12 | 211 | 1 | ✓ | all | 6 | ? |
| 3.12.440782 | 3 | 12 | 210 | 1 | ✓ | all | 6 | ? |
| 3.12.440783 | 3 | 12 | 210 | 1 | ✓ | all | 6 | ? |
| 3.12.440790 | 3 | 12 | 210 | 1 | ✓ | all | 6 | ? |
| 3.12.440807 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |