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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.
3,622,905 matroids, showing 19,801–19,850
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.11.75476 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.75499 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.75522 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.75541 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.75543 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.75545 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.75551 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.75559 | 3 | 11 | 154 | 1 | ✓ | all | 4 | rational |
| 3.11.75597 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.75598 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.75599 | 3 | 11 | 154 | 1 | ✓ | all | 4 | rational |
| 3.11.75600 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.75601 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.75602 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.75607 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.75609 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.75619 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.75620 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.75621 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.75622 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.75623 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.75624 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.75626 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.75627 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.75628 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.75629 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.75630 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.75632 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.75633 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.75636 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.75637 | 3 | 11 | 152 | 1 | ✓ | all | 4 | empty |
| 3.11.75638 | 3 | 11 | 151 | 1 | ✓ | all | 4 | empty |
| 3.11.75639 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.75640 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.75641 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.75647 | 3 | 11 | 151 | 1 | ✓ | all | 4 | empty |
| 3.11.75648 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.75650 | 3 | 11 | 154 | 1 | ✓ | all | 4 | rational |
| 3.11.75660 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.75661 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.75662 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.75663 | 3 | 11 | 154 | 1 | ✓ | all | 4 | rational |
| 3.11.75664 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.75665 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.75667 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.75668 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.75669 | 3 | 11 | 154 | 1 | ✓ | all | 4 | rational |
| 3.11.75670 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.75671 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.75673 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |