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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.
5,849,183 matroids, showing 21,701–21,750
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.11.181360 | 3 | 11 | 148 | 2 | ✓ | all but 2 | 1 | rational |
| 3.11.181362 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.181363 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.181364 | 3 | 11 | 149 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.181366 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.181368 | 3 | 11 | 148 | 1 | ✓ | all but 2,3 | 1 | rational |
| 3.11.181376 | 3 | 11 | 149 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.181377 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.181379 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.181380 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.181383 | 3 | 11 | 149 | 2 | ✓ | all but 2 | 1 | rational |
| 3.11.181384 | 3 | 11 | 149 | 2 | ✓ | all but 2 | 1 | rational |
| 3.11.181390 | 3 | 11 | 150 | 2 | ✓ | all but 2 | 1 | rational |
| 3.11.181391 | 3 | 11 | 150 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.181393 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.181394 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.181396 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.181397 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.181399 | 3 | 11 | 149 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.181400 | 3 | 11 | 150 | 2 | ✓ | all but 2,3 | 1 | rational |
| 3.11.181402 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.181403 | 3 | 11 | 149 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.181404 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.181407 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.181411 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.181485 | 3 | 11 | 150 | 2 | ✓ | all | 1 | rational |
| 3.11.181486 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.181487 | 3 | 11 | 150 | 2 | ✓ | all | 1 | rational |
| 3.11.181489 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.181490 | 3 | 11 | 150 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.181491 | 3 | 11 | 151 | 2 | ✓ | all | 1 | rational |
| 3.11.181493 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.181494 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.181495 | 3 | 11 | 149 | 2 | ✓ | all | 1 | rational |
| 3.11.181497 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.181498 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.181502 | 3 | 11 | 149 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.181503 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.181505 | 3 | 11 | 150 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.181506 | 3 | 11 | 149 | 2 | ✓ | all | 1 | rational |
| 3.11.181529 | 3 | 11 | 150 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.181530 | 3 | 11 | 150 | 2 | ✓ | all | 1 | rational |
| 3.11.181532 | 3 | 11 | 151 | 1 | ✓ | all | 1 | rational |
| 3.11.181533 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.181535 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.181541 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.181542 | 3 | 11 | 151 | 2 | ✓ | all but 2 | 1 | rational |
| 3.11.181544 | 3 | 11 | 149 | 2 | ✓ | all | 1 | rational |
| 3.11.181545 | 3 | 11 | 148 | 2 | ✓ | all but 2 | 1 | rational |
| 3.11.181550 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |