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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 19,451–19,500
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.11.7507 | 3 | 11 | 154 | 1 | ✓ | ∅ | -1 | empty |
| 3.11.7508 | 3 | 11 | 156 | 2 | ✓ | all | 5 | rational |
| 3.11.7509 | 3 | 11 | 155 | 2 | ✓ | all | 4 | rational |
| 3.11.7510 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7511 | 3 | 11 | 155 | 2 | ✓ | all | 4 | rational |
| 3.11.7512 | 3 | 11 | 157 | 1 | ✓ | all | 6 | rational |
| 3.11.7513 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7514 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7515 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7516 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7517 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7518 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7519 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7520 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7521 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7522 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7523 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7524 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7525 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7526 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7527 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7528 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7529 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7530 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7531 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7532 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7533 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7534 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7535 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7536 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7537 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7538 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7539 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7540 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7541 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7542 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7543 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7544 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7545 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7546 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7547 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7548 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7549 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7550 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7551 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7552 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7553 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7554 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7555 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |
| 3.11.7556 | 3 | 11 | 154 | 1 | ✓ | all | 3 | rational |