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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.
2,030,492 matroids, showing 18,801–18,850
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.12.125086 | 3 | 12 | 209 | 2 | ✓ | all but 2,3 | 0 | ? |
| 3.12.125088 | 3 | 12 | 209 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.125117 | 3 | 12 | 211 | 1 | ✓ | all but 2,7 | 0 | ? |
| 3.12.125122 | 3 | 12 | 210 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.125136 | 3 | 12 | 210 | 2 | ✓ | all but 2,3 | 0 | ? |
| 3.12.125137 | 3 | 12 | 210 | 1 | ✓ | all | 0 | ? |
| 3.12.125152 | 3 | 12 | 210 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.125162 | 3 | 12 | 209 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.125175 | 3 | 12 | 209 | 2 | ✓ | all but 2,3,7 | 0 | ? |
| 3.12.125184 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.125185 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.125200 | 3 | 12 | 210 | 1 | ✓ | all but 2,3,5,7,11 | 0 | ? |
| 3.12.125211 | 3 | 12 | 210 | 1 | ✓ | all but 2,3,7 | 0 | ? |
| 3.12.125215 | 3 | 12 | 210 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.125241 | 3 | 12 | 210 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.125257 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5,7 | 0 | ? |
| 3.12.125264 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5,7,11 | 0 | ? |
| 3.12.125267 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.125273 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,7 | 0 | ? |
| 3.12.125286 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.125294 | 3 | 12 | 210 | 1 | ✓ | all but 2,5,11 | 0 | ? |
| 3.12.125300 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,7 | 0 | ? |
| 3.12.125301 | 3 | 12 | 210 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.125306 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.125347 | 3 | 12 | 209 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.125388 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.125399 | 3 | 12 | 209 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.125406 | 3 | 12 | 210 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.125407 | 3 | 12 | 209 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.125413 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.125416 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,11 | 0 | ? |
| 3.12.125422 | 3 | 12 | 208 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.125426 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,7 | 0 | ? |
| 3.12.125429 | 3 | 12 | 209 | 1 | ✓ | all but 2,29 | 0 | ? |
| 3.12.125460 | 3 | 12 | 208 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.125489 | 3 | 12 | 209 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.125509 | 3 | 12 | 209 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.125514 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.125515 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5,7 | 0 | ? |
| 3.12.125518 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.125522 | 3 | 12 | 208 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.125524 | 3 | 12 | 208 | 1 | ✓ | all | 0 | ? |
| 3.12.125532 | 3 | 12 | 208 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.125543 | 3 | 12 | 208 | 2 | ✓ | all but 2,3 | 0 | ? |
| 3.12.125545 | 3 | 12 | 208 | 1 | ✓ | all | 0 | ? |
| 3.12.125546 | 3 | 12 | 209 | 1 | ✓ | all but 2,11 | 0 | ? |
| 3.12.125560 | 3 | 12 | 209 | 1 | ✓ | all | 0 | ? |
| 3.12.125579 | 3 | 12 | 210 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.125615 | 3 | 12 | 208 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.125627 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |