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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.
1,370,992 matroids, showing 19,301–19,350
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.11.262492 | 3 | 11 | 141 | 1 | ✓ | all | 5 | rational |
| 3.11.262493 | 3 | 11 | 140 | 1 | ✓ | all | 5 | rational |
| 3.11.262495 | 3 | 11 | 141 | 2 | ✓ | all | 5 | rational |
| 3.11.262497 | 3 | 11 | 143 | 1 | ✓ | all | 5 | rational |
| 3.11.262499 | 3 | 11 | 142 | 1 | ✓ | all | 5 | rational |
| 3.11.262501 | 3 | 11 | 142 | 1 | ✓ | all | 5 | rational |
| 3.11.262503 | 3 | 11 | 141 | 1 | ✓ | all | 5 | rational |
| 3.11.262505 | 3 | 11 | 141 | 1 | ✓ | all | 5 | empty |
| 3.11.262506 | 3 | 11 | 141 | 1 | ✓ | all | 5 | rational |
| 3.11.262508 | 3 | 11 | 141 | 2 | ✓ | all | 5 | rational |
| 3.11.262511 | 3 | 11 | 141 | 1 | ✓ | all | 5 | rational |
| 3.11.262515 | 3 | 11 | 142 | 1 | ✓ | all | 5 | rational |
| 3.11.262519 | 3 | 11 | 140 | 1 | ✓ | all | 5 | rational |
| 3.11.262521 | 3 | 11 | 141 | 1 | ✓ | all | 5 | rational |
| 3.11.262523 | 3 | 11 | 143 | 1 | ✓ | all | 5 | rational |
| 3.11.262525 | 3 | 11 | 142 | 1 | ✓ | all | 5 | rational |
| 3.11.262527 | 3 | 11 | 142 | 1 | ✓ | all | 5 | rational |
| 3.11.262533 | 3 | 11 | 141 | 1 | ✓ | all | 5 | rational |
| 3.11.262534 | 3 | 11 | 142 | 1 | ✓ | all | 5 | rational |
| 3.11.262535 | 3 | 11 | 141 | 1 | ✓ | all | 5 | rational |
| 3.11.262536 | 3 | 11 | 141 | 1 | ✓ | all | 5 | rational |
| 3.11.262537 | 3 | 11 | 141 | 1 | ✓ | all | 5 | rational |
| 3.11.262538 | 3 | 11 | 140 | 1 | ✓ | all | 5 | point over Q(a)/(a^2 + 1) |
| 3.11.262539 | 3 | 11 | 142 | 1 | ✓ | all | 5 | rational |
| 3.11.262545 | 3 | 11 | 141 | 1 | ✓ | all | 5 | rational |
| 3.11.262564 | 3 | 11 | 140 | 1 | ✓ | all | 5 | rational |
| 3.11.262565 | 3 | 11 | 141 | 1 | ✓ | all | 5 | rational |
| 3.11.262566 | 3 | 11 | 140 | 1 | ✓ | all | 5 | point over Q(a)/(a^2 + 1) |
| 3.11.262567 | 3 | 11 | 140 | 1 | ✓ | all | 5 | rational |
| 3.11.262568 | 3 | 11 | 140 | 1 | ✓ | all | 5 | rational |
| 3.11.262569 | 3 | 11 | 139 | 1 | ✓ | all | 5 | empty |
| 3.11.262570 | 3 | 11 | 141 | 1 | ✓ | all | 5 | rational over Q(a)/(a^2 - a + 1) |
| 3.11.262571 | 3 | 11 | 140 | 1 | ✓ | all | 5 | point over Q(a)/(a^2 - a + 1) |
| 3.11.262572 | 3 | 11 | 140 | 1 | ✓ | all | 5 | point over Q(a)/(a^2 - a + 1) |
| 3.11.262580 | 3 | 11 | 141 | 1 | ✓ | all | 5 | rational |
| 3.11.262594 | 3 | 11 | 141 | 1 | ✓ | all | 5 | rational |
| 3.11.262613 | 3 | 11 | 143 | 1 | ✓ | all | 5 | rational |
| 3.11.262639 | 3 | 11 | 142 | 1 | ✓ | all | 5 | rational |
| 3.11.262667 | 3 | 11 | 141 | 2 | ✓ | all | 5 | rational |
| 3.11.262722 | 3 | 11 | 140 | 1 | ✓ | all | 5 | empty |
| 3.11.262793 | 3 | 11 | 139 | 2 | ✓ | all | 5 | rational |
| 3.11.262812 | 3 | 11 | 139 | 1 | ✓ | all | 5 | rational |
| 3.11.262886 | 3 | 11 | 140 | 4 | ✓ | all | 5 | rational |
| 3.11.262887 | 3 | 11 | 141 | 32 | ✓ | all | 5 | rational |
| 3.11.262888 | 3 | 11 | 140 | 8 | ✓ | all | 5 | rational |
| 3.11.262889 | 3 | 11 | 140 | 32 | ✓ | all | 5 | empty |
| 3.11.262890 | 3 | 11 | 140 | 8 | ✓ | all | 5 | rational |
| 3.11.262891 | 3 | 11 | 139 | 4 | ✓ | all | 5 | rational |
| 3.11.262892 | 3 | 11 | 139 | 4 | ✓ | all | 5 | rational |
| 3.11.262893 | 3 | 11 | 142 | 12 | ✓ | all | 5 | rational |