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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 19,601–19,650
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.11.7657 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7658 | 3 | 11 | 153 | 1 | ✓ | ∅ | -1 | empty |
| 3.11.7659 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7660 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7661 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7662 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7663 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7664 | 3 | 11 | 153 | 1 | ✓ | all | 2 | rational |
| 3.11.7665 | 3 | 11 | 158 | 12 | ✓ | all | 7 | rational |
| 3.11.7666 | 3 | 11 | 157 | 4 | ✓ | all | 6 | rational |
| 3.11.7667 | 3 | 11 | 157 | 4 | ✓ | all | 6 | rational |
| 3.11.7668 | 3 | 11 | 157 | 4 | ✓ | all | 6 | rational |
| 3.11.7669 | 3 | 11 | 157 | 1 | ✓ | all | 6 | rational |
| 3.11.7670 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7671 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7672 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7673 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7674 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7675 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7676 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7677 | 3 | 11 | 156 | 2 | ✓ | all | 5 | rational |
| 3.11.7678 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7679 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7680 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7681 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7682 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7683 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7684 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7685 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7686 | 3 | 11 | 156 | 2 | ✓ | all | 5 | rational |
| 3.11.7687 | 3 | 11 | 155 | 2 | ✓ | all | 4 | rational |
| 3.11.7688 | 3 | 11 | 155 | 2 | ✓ | all | 4 | rational |
| 3.11.7689 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7690 | 3 | 11 | 155 | 2 | ✓ | all | 4 | rational |
| 3.11.7691 | 3 | 11 | 156 | 2 | ✓ | all | 5 | rational |
| 3.11.7692 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7693 | 3 | 11 | 155 | 2 | ✓ | all | 4 | rational |
| 3.11.7694 | 3 | 11 | 155 | 2 | ✓ | all | 4 | rational |
| 3.11.7695 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7696 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7697 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7698 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7699 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7700 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7701 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7702 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7703 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7704 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7705 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7706 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |