Search
…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 20,701–20,750
| label ▼ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 4.9.169513 | 4 | 9 | 108 | 1 | ✓ | all | 4 | rational |
| 4.9.169512 | 4 | 9 | 106 | 1 | ✓ | all | 2 | rational |
| 4.9.169511 | 4 | 9 | 106 | 1 | ✓ | all | 1 | rational |
| 4.9.169510 | 4 | 9 | 107 | 1 | ✓ | all | 2 | rational |
| 4.9.169509 | 4 | 9 | 106 | 1 | ✓ | all | 3 | rational |
| 4.9.169508 | 4 | 9 | 107 | 1 | ✓ | all | 4 | rational |
| 4.9.169507 | 4 | 9 | 106 | 1 | ✓ | all but 2 | 1 | rational |
| 4.9.169506 | 4 | 9 | 106 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169505 | 4 | 9 | 107 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169504 | 4 | 9 | 107 | 1 | ✓ | all | 5 | rational |
| 4.9.169503 | 4 | 9 | 107 | 1 | ✓ | all | 2 | rational |
| 4.9.169502 | 4 | 9 | 108 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169501 | 4 | 9 | 105 | 1 | ✓ | all but 2,3,5,7 | 0 | point over Q(a)/(a^2 + 1) |
| 4.9.169500 | 4 | 9 | 106 | 1 | ✓ | all | 4 | rational |
| 4.9.169499 | 4 | 9 | 106 | 1 | ✓ | all | 3 | rational |
| 4.9.169498 | 4 | 9 | 106 | 1 | ✓ | all | 1 | rational |
| 4.9.169497 | 4 | 9 | 107 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169496 | 4 | 9 | 106 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169495 | 4 | 9 | 106 | 1 | ✓ | all | 3 | rational |
| 4.9.169494 | 4 | 9 | 107 | 1 | ✓ | all but 2,3,5 | 1 | rational |
| 4.9.169493 | 4 | 9 | 106 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169492 | 4 | 9 | 107 | 1 | ✓ | all | 3 | rational |
| 4.9.169491 | 4 | 9 | 107 | 1 | ✓ | all but 2,3 | 1 | rational |
| 4.9.169490 | 4 | 9 | 107 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169489 | 4 | 9 | 108 | 1 | ✓ | all | 4 | rational |
| 4.9.169488 | 4 | 9 | 106 | 1 | ✓ | all | 3 | rational |
| 4.9.169487 | 4 | 9 | 107 | 1 | ✓ | all but 2,3,5 | 0 | rational |
| 4.9.169486 | 4 | 9 | 107 | 1 | ✓ | all | 4 | rational |
| 4.9.169485 | 4 | 9 | 107 | 1 | ✓ | all | 1 | rational |
| 4.9.169484 | 4 | 9 | 107 | 1 | ✓ | all but 2 | 1 | rational |
| 4.9.169483 | 4 | 9 | 108 | 1 | ✓ | all | 2 | rational |
| 4.9.169482 | 4 | 9 | 107 | 1 | ✓ | all | 3 | rational |
| 4.9.169481 | 4 | 9 | 107 | 1 | ✓ | all | 2 | rational |
| 4.9.169480 | 4 | 9 | 108 | 1 | ✓ | all | 2 | rational |
| 4.9.169479 | 4 | 9 | 107 | 1 | ✓ | all | 1 | rational |
| 4.9.169478 | 4 | 9 | 108 | 1 | ✓ | all | 2 | rational |
| 4.9.169477 | 4 | 9 | 107 | 1 | ✓ | all | 1 | rational |
| 4.9.169476 | 4 | 9 | 107 | 1 | ✓ | all | 3 | rational |
| 4.9.169475 | 4 | 9 | 108 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169474 | 4 | 9 | 108 | 1 | ✓ | all | 0 | rational |
| 4.9.169473 | 4 | 9 | 108 | 1 | ✓ | all | 3 | rational |
| 4.9.169472 | 4 | 9 | 108 | 1 | ✓ | all | 4 | rational |
| 4.9.169471 | 4 | 9 | 109 | 1 | ✓ | all | 3 | rational |
| 4.9.169470 | 4 | 9 | 106 | 1 | ✓ | all | 4 | rational |
| 4.9.169469 | 4 | 9 | 107 | 1 | ✓ | all | 2 | rational |
| 4.9.169468 | 4 | 9 | 106 | 1 | ✓ | all | 3 | rational |
| 4.9.169467 | 4 | 9 | 107 | 1 | ✓ | all | 2 | rational |
| 4.9.169466 | 4 | 9 | 105 | 1 | ✓ | all | 2 | point over Q(a)/(a^2 + 1) |
| 4.9.169465 | 4 | 9 | 106 | 1 | ✓ | all | 3 | rational |
| 4.9.169464 | 4 | 9 | 106 | 1 | ✓ | all | 2 | rational |