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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.
32,400,859 matroids, showing 19,551–19,600
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.11.7607 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7608 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7609 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7610 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7611 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7612 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7613 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7614 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7615 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7616 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7617 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7618 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7619 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7620 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7621 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7622 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7623 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7624 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7625 | 3 | 11 | 154 | 1 | ✓ | ∅ | -1 | empty |
| 3.11.7626 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7627 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7628 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7629 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7630 | 3 | 11 | 154 | 2 | ✓ | all | 3 | rational |
| 3.11.7631 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7632 | 3 | 11 | 153 | 1 | ✓ | all | 2 | rational |
| 3.11.7633 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7634 | 3 | 11 | 153 | 2 | ✓ | all | 2 | rational |
| 3.11.7635 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7636 | 3 | 11 | 153 | 1 | ✓ | ∅ | -1 | empty |
| 3.11.7637 | 3 | 11 | 153 | 1 | ✓ | all | 2 | rational |
| 3.11.7638 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7639 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7640 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7641 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7642 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7643 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7644 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7645 | 3 | 11 | 153 | 3 | ✓ | all | 2 | K3 surface |
| 3.11.7646 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7647 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7648 | 3 | 11 | 153 | 1 | ✓ | ∅ | -1 | empty |
| 3.11.7649 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7650 | 3 | 11 | 154 | 1 | ✓ | ∅ | -1 | empty |
| 3.11.7651 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7652 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7653 | 3 | 11 | 154 | 1 | ✓ | ∅ | -1 | empty |
| 3.11.7654 | 3 | 11 | 153 | 2 | ✓ | all | 3 | rational |
| 3.11.7655 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7656 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |