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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.
381,906 matroids, showing 18,901–18,950
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.12.361596 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.361597 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.361601 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.361613 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.361628 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.361640 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.361642 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.361692 | 3 | 12 | 210 | 1 | ✓ | all | 6 | ? |
| 3.12.361698 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.361745 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.361755 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.361778 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.361805 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.361838 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.361881 | 3 | 12 | 211 | 1 | ✓ | all | 6 | ? |
| 3.12.361882 | 3 | 12 | 210 | 1 | ✓ | all | 6 | ? |
| 3.12.361932 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.361972 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.361976 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.361996 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.362086 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.362095 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.362110 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.362115 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.362124 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.362134 | 3 | 12 | 210 | 1 | ✓ | all | 6 | ? |
| 3.12.362143 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.362194 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.362195 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.362255 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.362277 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.362320 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.362321 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.362362 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.362420 | 3 | 12 | 210 | 1 | ✓ | all | 6 | ? |
| 3.12.362459 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.362466 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.362470 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.362475 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.362478 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.362519 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.362554 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.362559 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.362579 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.362603 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.362615 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.362626 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.362695 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.362715 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.362720 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |