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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.
32,400,859 matroids, showing 19,301–19,350
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.11.7357 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7358 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7359 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7360 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7361 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7362 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7363 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7364 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7365 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7366 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7367 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7368 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7369 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7370 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7371 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7372 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7373 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7374 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7375 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7376 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7377 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7378 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7379 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7380 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7381 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7382 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7383 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7384 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7385 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7386 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7387 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7388 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7389 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7390 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7391 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7392 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7393 | 3 | 11 | 154 | 1 | ✓ | ∅ | -1 | empty |
| 3.11.7394 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7395 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7396 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7397 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7398 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7399 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7400 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7401 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7402 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7403 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7404 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7405 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7406 | 3 | 11 | 157 | 1 | ✓ | all | 6 | rational |