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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 22,551–22,600
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.11.186494 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.186495 | 3 | 11 | 147 | 1 | ✓ | all | 1 | point over Q(a)/(a^3 - a^2 + 1) |
| 3.11.186496 | 3 | 11 | 147 | 1 | ✓ | all | 1 | rational |
| 3.11.186497 | 3 | 11 | 146 | 1 | ✓ | all | 1 | rational |
| 3.11.186500 | 3 | 11 | 148 | 1 | ✓ | all but 2 | 1 | empty |
| 3.11.186503 | 3 | 11 | 147 | 1 | ✓ | all | 1 | empty |
| 3.11.186520 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.186526 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.186527 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.186533 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.186534 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.186569 | 3 | 11 | 150 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.186570 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.186571 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.186573 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.186574 | 3 | 11 | 149 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.186575 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.186576 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.186578 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.186579 | 3 | 11 | 149 | 1 | ✓ | all but 2,3 | 1 | rational |
| 3.11.186581 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.186591 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.186592 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.186594 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.186595 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.186596 | 3 | 11 | 149 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.186598 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.186599 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.186600 | 3 | 11 | 149 | 1 | ✓ | all but 2,3 | 1 | rational |
| 3.11.186602 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.186609 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.186612 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.186613 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.186625 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.186626 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.186627 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.186630 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.186631 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.186632 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.186634 | 3 | 11 | 149 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.186636 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.186638 | 3 | 11 | 149 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.186639 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.186640 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.186641 | 3 | 11 | 147 | 1 | ✓ | all | 1 | rational |
| 3.11.186642 | 3 | 11 | 147 | 1 | ✓ | all | 1 | rational |
| 3.11.186646 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.186652 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.186653 | 3 | 11 | 151 | 1 | ✓ | all | 1 | rational |
| 3.11.186654 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |