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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 22,651–22,700
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.12.451718 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.451820 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.451852 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.451881 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.451899 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.451921 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.451936 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.451961 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.451966 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.452021 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.452029 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.452054 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.452164 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.452250 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.452251 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.452258 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.452261 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.452269 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.452276 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.452278 | 3 | 12 | 206 | 1 | ✓ | all | 6 | ? |
| 3.12.452306 | 3 | 12 | 210 | 1 | ✓ | all | 6 | ? |
| 3.12.452327 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.452374 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.452376 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.452391 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.452426 | 3 | 12 | 208 | 2 | ✓ | all | 6 | ? |
| 3.12.452437 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.452454 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.452483 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.452495 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.452582 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.452583 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.452607 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.452625 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.452636 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.452642 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.452667 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.452681 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.452683 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.452706 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.452710 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.452791 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.452806 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.452809 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.452860 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.452870 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.452899 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.452902 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.452969 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.452999 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |