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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 19,251–19,300
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.12.369608 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.369617 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.369620 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.369712 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.369721 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.369739 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.369741 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.369761 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.369771 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.369801 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.369804 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.369809 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.369816 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.369817 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.369825 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.369833 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.369838 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.369844 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.369846 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.369875 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.369882 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.369912 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.369921 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.369930 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.369931 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.369973 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.370010 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.370042 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.370061 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.370076 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.370129 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.370140 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.370152 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.370153 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.370170 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.370173 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.370208 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.370217 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.370234 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.370249 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.370265 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.370285 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.370297 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.370316 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.370343 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.370392 | 3 | 12 | 206 | 1 | ✓ | all | 6 | ? |
| 3.12.370411 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.370424 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.370449 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.370456 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |