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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.
2,030,492 matroids, showing 18,901–18,950
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.12.126037 | 3 | 12 | 208 | 1 | ✓ | all | 0 | ? |
| 3.12.126038 | 3 | 12 | 208 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.126041 | 3 | 12 | 208 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.126051 | 3 | 12 | 210 | 1 | ✓ | all but 2,3,11 | 0 | ? |
| 3.12.126091 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,7 | 0 | ? |
| 3.12.126092 | 3 | 12 | 210 | 1 | ✓ | all but 2,3,5,11 | 0 | ? |
| 3.12.126099 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.126104 | 3 | 12 | 208 | 1 | ✓ | all | 0 | ? |
| 3.12.126117 | 3 | 12 | 208 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.126142 | 3 | 12 | 208 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.126162 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.126170 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.126197 | 3 | 12 | 208 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.126222 | 3 | 12 | 211 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.126233 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.126242 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,7 | 0 | ? |
| 3.12.126245 | 3 | 12 | 209 | 2 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.126268 | 3 | 12 | 209 | 1 | ✓ | all | 0 | ? |
| 3.12.126274 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.126278 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.126280 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.126281 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,7 | 0 | ? |
| 3.12.126282 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.126296 | 3 | 12 | 209 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.126297 | 3 | 12 | 208 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.126315 | 3 | 12 | 208 | 1 | ✓ | all | 0 | ? |
| 3.12.126319 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.126324 | 3 | 12 | 210 | 1 | ✓ | all | 0 | ? |
| 3.12.126339 | 3 | 12 | 208 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.126351 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,7 | 0 | ? |
| 3.12.126358 | 3 | 12 | 209 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.126359 | 3 | 12 | 209 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.126378 | 3 | 12 | 207 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.126387 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.126393 | 3 | 12 | 208 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.126397 | 3 | 12 | 208 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.126402 | 3 | 12 | 208 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.126409 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.126424 | 3 | 12 | 211 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.126425 | 3 | 12 | 210 | 1 | ✓ | all | 0 | ? |
| 3.12.126447 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5,7,13 | 0 | ? |
| 3.12.126451 | 3 | 12 | 210 | 1 | ✓ | all but 2,3,11 | 0 | ? |
| 3.12.126466 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5,7,11 | 0 | ? |
| 3.12.126474 | 3 | 12 | 210 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.126485 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5,7 | 0 | ? |
| 3.12.126514 | 3 | 12 | 209 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.126539 | 3 | 12 | 210 | 1 | ✓ | all but 2,7 | 0 | ? |
| 3.12.126541 | 3 | 12 | 210 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.126548 | 3 | 12 | 209 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.126582 | 3 | 12 | 209 | 1 | ✓ | all but 2,5 | 0 | ? |