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 20,651–20,700
| label ▼ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 4.9.169563 | 4 | 9 | 106 | 1 | ✓ | all | 2 | rational |
| 4.9.169562 | 4 | 9 | 107 | 1 | ✓ | all | 2 | rational |
| 4.9.169561 | 4 | 9 | 107 | 1 | ✓ | all | 1 | rational |
| 4.9.169560 | 4 | 9 | 107 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169559 | 4 | 9 | 108 | 1 | ✓ | all | 3 | rational |
| 4.9.169558 | 4 | 9 | 106 | 1 | ✓ | all | 4 | rational |
| 4.9.169557 | 4 | 9 | 106 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169556 | 4 | 9 | 106 | 1 | ✓ | all | 4 | rational |
| 4.9.169555 | 4 | 9 | 107 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169554 | 4 | 9 | 107 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169553 | 4 | 9 | 106 | 1 | ✓ | all | 4 | rational |
| 4.9.169552 | 4 | 9 | 107 | 1 | ✓ | all | 3 | rational |
| 4.9.169551 | 4 | 9 | 106 | 1 | ✓ | all | 2 | rational |
| 4.9.169550 | 4 | 9 | 107 | 1 | ✓ | all | 4 | rational |
| 4.9.169549 | 4 | 9 | 107 | 1 | ✓ | all | 4 | rational |
| 4.9.169548 | 4 | 9 | 107 | 1 | ✓ | all | 3 | rational |
| 4.9.169547 | 4 | 9 | 108 | 1 | ✓ | all | 4 | rational |
| 4.9.169546 | 4 | 9 | 107 | 1 | ✓ | all | 4 | rational |
| 4.9.169545 | 4 | 9 | 107 | 1 | ✓ | all | 3 | rational |
| 4.9.169544 | 4 | 9 | 107 | 1 | ✓ | all | 5 | rational |
| 4.9.169543 | 4 | 9 | 108 | 1 | ✓ | all | 2 | rational |
| 4.9.169542 | 4 | 9 | 107 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169541 | 4 | 9 | 107 | 1 | ✓ | all | 1 | rational |
| 4.9.169540 | 4 | 9 | 108 | 1 | ✓ | all | 1 | rational |
| 4.9.169539 | 4 | 9 | 107 | 1 | ✓ | all | 4 | rational |
| 4.9.169538 | 4 | 9 | 108 | 1 | ✓ | all but 2,3,5 | 0 | rational |
| 4.9.169537 | 4 | 9 | 106 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169536 | 4 | 9 | 107 | 1 | ✓ | all | 3 | rational |
| 4.9.169535 | 4 | 9 | 107 | 1 | ✓ | all | 5 | rational |
| 4.9.169534 | 4 | 9 | 107 | 1 | ✓ | all | 2 | rational |
| 4.9.169533 | 4 | 9 | 108 | 1 | ✓ | all but 2 | 1 | rational |
| 4.9.169532 | 4 | 9 | 107 | 1 | ✓ | all | 1 | rational |
| 4.9.169531 | 4 | 9 | 107 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169530 | 4 | 9 | 108 | 1 | ✓ | all | 3 | rational |
| 4.9.169529 | 4 | 9 | 108 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169528 | 4 | 9 | 108 | 1 | ✓ | all | 3 | rational |
| 4.9.169527 | 4 | 9 | 108 | 1 | ✓ | all | 4 | rational |
| 4.9.169526 | 4 | 9 | 109 | 1 | ✓ | all | 4 | rational |
| 4.9.169525 | 4 | 9 | 106 | 1 | ✓ | all | 2 | rational over Q(a)/(a^2 - a + 1) |
| 4.9.169524 | 4 | 9 | 105 | 1 | ✓ | ∅ | -1 | empty |
| 4.9.169523 | 4 | 9 | 106 | 1 | ✓ | all | 4 | rational over Q(a)/(a^2 - a + 1) |
| 4.9.169522 | 4 | 9 | 106 | 1 | ✓ | all but 2,3 | 1 | rational over Q(a)/(a^2 - a + 1) |
| 4.9.169521 | 4 | 9 | 107 | 1 | ✓ | ∅ | -1 | rational over Q(a)/(a^2 - a + 1) |
| 4.9.169520 | 4 | 9 | 106 | 1 | ✓ | all | 5 | rational |
| 4.9.169519 | 4 | 9 | 107 | 1 | ✓ | all | 4 | rational |
| 4.9.169518 | 4 | 9 | 107 | 1 | ✓ | all | 4 | rational |
| 4.9.169517 | 4 | 9 | 106 | 1 | ✓ | ∅ | -1 | empty |
| 4.9.169516 | 4 | 9 | 107 | 1 | ✓ | all | 3 | rational |
| 4.9.169515 | 4 | 9 | 107 | 1 | ✓ | all | 1 | rational |
| 4.9.169514 | 4 | 9 | 107 | 1 | ✓ | all but 2,3 | 0 | rational |