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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.
6,662,718 matroids, showing 21,201–21,250
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.11.71604 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71606 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71607 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71608 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71616 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71617 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71618 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71620 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71621 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.71622 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.71624 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.71625 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.71626 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.71635 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.71636 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71637 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71638 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71640 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.71641 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71642 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71643 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71645 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71646 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71647 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71648 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71649 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71651 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.71652 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71653 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71654 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71656 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71657 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71658 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71659 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71660 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71663 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71666 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71673 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71675 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71677 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71679 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71680 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71681 | 3 | 11 | 153 | 1 | ✓ | all | 3 | rational |
| 3.11.71682 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71690 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71691 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71692 | 3 | 11 | 151 | 1 | ✓ | all | 3 | rational |
| 3.11.71693 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |
| 3.11.71695 | 3 | 11 | 151 | 1 | ✓ | all but 2 | 3 | rational |
| 3.11.71696 | 3 | 11 | 152 | 1 | ✓ | all | 3 | rational |