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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 19,501–19,550
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.11.7557 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7558 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7559 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7560 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7561 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7562 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7563 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7564 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7565 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7566 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7567 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7568 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7569 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7570 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7571 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7572 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7573 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7574 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7575 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7576 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7577 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7578 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7579 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7580 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7581 | 3 | 11 | 155 | 2 | ✓ | all | 4 | rational |
| 3.11.7582 | 3 | 11 | 154 | 2 | ✓ | all | 3 | rational |
| 3.11.7583 | 3 | 11 | 154 | 2 | ✓ | all | 3 | rational |
| 3.11.7584 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7585 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7586 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7587 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7588 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7589 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7590 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7591 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7592 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7593 | 3 | 11 | 154 | 1 | ✓ | ∅ | -1 | empty |
| 3.11.7594 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7595 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7596 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7597 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7598 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7599 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7600 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7601 | 3 | 11 | 154 | 1 | ✓ | ∅ | -1 | empty |
| 3.11.7602 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7603 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7604 | 3 | 11 | 154 | 1 | ✓ | all | 3 | K3 surface x P^1 |
| 3.11.7605 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7606 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |