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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 18,551–18,600
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.12.351549 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.351552 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.351594 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.351769 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.351781 | 3 | 12 | 210 | 1 | ✓ | all | 6 | ? |
| 3.12.351787 | 3 | 12 | 210 | 1 | ✓ | all | 6 | ? |
| 3.12.351828 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.351829 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.351839 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.351869 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.351885 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.351892 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.351902 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.351904 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.351919 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.351940 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.351953 | 3 | 12 | 210 | 1 | ✓ | all | 6 | ? |
| 3.12.351960 | 3 | 12 | 210 | 1 | ✓ | all | 6 | ? |
| 3.12.352016 | 3 | 12 | 210 | 1 | ✓ | all | 6 | ? |
| 3.12.352041 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.352054 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.352076 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.352108 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.352109 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.352112 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.352124 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.352258 | 3 | 12 | 210 | 1 | ✓ | all | 6 | ? |
| 3.12.352269 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.352270 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.352284 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.352302 | 3 | 12 | 211 | 1 | ✓ | all | 6 | ? |
| 3.12.352313 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.352317 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.352335 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.352402 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.352412 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.352428 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.352446 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.352494 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.352502 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.352506 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.352524 | 3 | 12 | 209 | 2 | ✓ | all | 6 | ? |
| 3.12.352536 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.352555 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.352566 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.352623 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.352627 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.352636 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.352667 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.352674 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |