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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 19,101–19,150
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.12.367250 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.367265 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.367267 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.367294 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.367298 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.367301 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.367306 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.367309 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.367325 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.367326 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.367330 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.367335 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.367337 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.367342 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.367350 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.367357 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.367362 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.367369 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.367376 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.367381 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.367385 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.367398 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.367442 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.367462 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.367464 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.367481 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.367483 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.367486 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.367509 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.367523 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.367539 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.367540 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.367554 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.367558 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.367560 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.367576 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.367577 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.367580 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.367588 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.367593 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.367599 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.367604 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.367605 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.367607 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.367610 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.367629 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.367633 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.367634 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.367645 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.367647 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |