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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 19,851–19,900
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.11.75674 | 3 | 11 | 154 | 1 | ✓ | all | 4 | rational |
| 3.11.75676 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.75677 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.75678 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.75679 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.75680 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.75681 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.75682 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.75689 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.75690 | 3 | 11 | 154 | 1 | ✓ | all | 4 | rational |
| 3.11.75691 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.75692 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.75693 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.75694 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.75700 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.75701 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.75703 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.75709 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.75711 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.75712 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.75713 | 3 | 11 | 154 | 1 | ✓ | all | 4 | rational |
| 3.11.75716 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.75718 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.75721 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.75731 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.75732 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.75733 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.75734 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.75735 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.75736 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.75738 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.75739 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.75740 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.75741 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.75742 | 3 | 11 | 152 | 1 | ✓ | all | 4 | empty |
| 3.11.75744 | 3 | 11 | 151 | 1 | ✓ | all | 4 | empty |
| 3.11.75745 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.75746 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.75747 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.75749 | 3 | 11 | 154 | 2 | ✓ | all | 4 | rational |
| 3.11.75750 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.75751 | 3 | 11 | 152 | 2 | ✓ | all | 4 | rational |
| 3.11.75752 | 3 | 11 | 153 | 2 | ✓ | all | 4 | rational |
| 3.11.75753 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.75754 | 3 | 11 | 152 | 2 | ✓ | all | 4 | rational |
| 3.11.75755 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.75760 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.75764 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.75765 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.75766 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |