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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.
1,370,992 matroids, showing 18,651–18,700
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.11.256655 | 3 | 11 | 146 | 1 | ✓ | all | 5 | rational |
| 3.11.256656 | 3 | 11 | 147 | 1 | ✓ | all | 5 | rational |
| 3.11.256657 | 3 | 11 | 146 | 1 | ✓ | all | 5 | rational |
| 3.11.256659 | 3 | 11 | 146 | 1 | ✓ | all | 5 | rational |
| 3.11.256660 | 3 | 11 | 146 | 1 | ✓ | all | 5 | rational |
| 3.11.256661 | 3 | 11 | 146 | 1 | ✓ | all | 5 | rational |
| 3.11.256662 | 3 | 11 | 146 | 1 | ✓ | all | 5 | rational |
| 3.11.256663 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.256664 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.256665 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.256671 | 3 | 11 | 146 | 1 | ✓ | all | 5 | rational |
| 3.11.256673 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.256674 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.256675 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.256676 | 3 | 11 | 146 | 1 | ✓ | all | 5 | rational |
| 3.11.256677 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.256678 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.256679 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.256685 | 3 | 11 | 147 | 2 | ✓ | all | 5 | rational |
| 3.11.256690 | 3 | 11 | 147 | 2 | ✓ | all | 5 | rational |
| 3.11.256692 | 3 | 11 | 146 | 1 | ✓ | all | 5 | rational |
| 3.11.256693 | 3 | 11 | 146 | 2 | ✓ | all | 5 | rational |
| 3.11.256694 | 3 | 11 | 144 | 4 | ✓ | all | 5 | rational |
| 3.11.256695 | 3 | 11 | 148 | 1 | ✓ | all | 5 | rational |
| 3.11.256696 | 3 | 11 | 147 | 1 | ✓ | all | 5 | rational |
| 3.11.256697 | 3 | 11 | 147 | 1 | ✓ | all | 5 | rational |
| 3.11.256698 | 3 | 11 | 147 | 1 | ✓ | all | 5 | rational |
| 3.11.256704 | 3 | 11 | 146 | 1 | ✓ | all | 5 | rational |
| 3.11.256710 | 3 | 11 | 146 | 1 | ✓ | all | 5 | rational |
| 3.11.256716 | 3 | 11 | 147 | 1 | ✓ | all | 5 | rational |
| 3.11.256718 | 3 | 11 | 146 | 1 | ✓ | all | 5 | rational |
| 3.11.256719 | 3 | 11 | 146 | 1 | ✓ | all | 5 | rational |
| 3.11.256720 | 3 | 11 | 147 | 1 | ✓ | all | 5 | rational |
| 3.11.256721 | 3 | 11 | 146 | 1 | ✓ | all | 5 | rational |
| 3.11.256722 | 3 | 11 | 146 | 1 | ✓ | all | 5 | rational |
| 3.11.256723 | 3 | 11 | 146 | 1 | ✓ | all | 5 | rational |
| 3.11.256727 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.256730 | 3 | 11 | 146 | 1 | ✓ | all | 5 | rational |
| 3.11.256734 | 3 | 11 | 147 | 1 | ✓ | all | 5 | rational |
| 3.11.256735 | 3 | 11 | 146 | 1 | ✓ | all | 5 | rational |
| 3.11.256736 | 3 | 11 | 146 | 1 | ✓ | all | 5 | rational |
| 3.11.256737 | 3 | 11 | 146 | 1 | ✓ | all | 5 | rational |
| 3.11.256738 | 3 | 11 | 146 | 1 | ✓ | all | 5 | rational |
| 3.11.256739 | 3 | 11 | 146 | 1 | ✓ | all | 5 | rational |
| 3.11.256740 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.256746 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.256751 | 3 | 11 | 146 | 1 | ✓ | all | 5 | rational |
| 3.11.256756 | 3 | 11 | 146 | 2 | ✓ | all | 5 | empty |
| 3.11.256761 | 3 | 11 | 145 | 2 | ✓ | all | 5 | rational |
| 3.11.256765 | 3 | 11 | 146 | 1 | ✓ | all | 5 | rational |