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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 19,001–19,050
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.11.258403 | 3 | 11 | 144 | 1 | ✓ | all | 5 | rational |
| 3.11.258404 | 3 | 11 | 144 | 1 | ✓ | all | 5 | rational |
| 3.11.258406 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.258408 | 3 | 11 | 144 | 1 | ✓ | all | 5 | rational |
| 3.11.258411 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.258416 | 3 | 11 | 144 | 1 | ✓ | all | 5 | rational |
| 3.11.258421 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.258433 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.258452 | 3 | 11 | 145 | 2 | ✓ | all | 5 | rational |
| 3.11.258471 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.258482 | 3 | 11 | 144 | 2 | ✓ | all | 5 | rational |
| 3.11.258483 | 3 | 11 | 143 | 2 | ✓ | all | 5 | rational |
| 3.11.258484 | 3 | 11 | 147 | 1 | ✓ | all | 5 | rational |
| 3.11.258485 | 3 | 11 | 146 | 1 | ✓ | all | 5 | rational |
| 3.11.258486 | 3 | 11 | 146 | 1 | ✓ | all | 5 | rational |
| 3.11.258487 | 3 | 11 | 146 | 1 | ✓ | all | 5 | rational |
| 3.11.258488 | 3 | 11 | 146 | 1 | ✓ | all | 5 | rational |
| 3.11.258493 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.258499 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.258504 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.258509 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.258514 | 3 | 11 | 144 | 1 | ✓ | all | 5 | rational |
| 3.11.258536 | 3 | 11 | 143 | 1 | ✓ | all | 5 | rational |
| 3.11.258553 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.258567 | 3 | 11 | 144 | 1 | ✓ | all | 5 | rational |
| 3.11.258568 | 3 | 11 | 144 | 1 | ✓ | all | 5 | rational |
| 3.11.258640 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.258689 | 3 | 11 | 144 | 1 | ✓ | all | 5 | rational |
| 3.11.258741 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.258771 | 3 | 11 | 144 | 1 | ✓ | all | 5 | rational |
| 3.11.258772 | 3 | 11 | 144 | 1 | ✓ | all | 5 | rational |
| 3.11.258774 | 3 | 11 | 143 | 2 | ✓ | all | 5 | rational |
| 3.11.258777 | 3 | 11 | 144 | 1 | ✓ | all | 5 | rational |
| 3.11.258781 | 3 | 11 | 142 | 1 | ✓ | all | 5 | rational |
| 3.11.258788 | 3 | 11 | 144 | 1 | ✓ | all | 5 | rational |
| 3.11.258792 | 3 | 11 | 143 | 1 | ✓ | all | 5 | rational |
| 3.11.258796 | 3 | 11 | 141 | 12 | ✓ | all | 5 | rational |
| 3.11.258804 | 3 | 11 | 146 | 4 | ✓ | all | 5 | rational |
| 3.11.258805 | 3 | 11 | 146 | 2 | ✓ | all | 5 | rational |
| 3.11.258806 | 3 | 11 | 146 | 1 | ✓ | all | 5 | rational |
| 3.11.258807 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.258808 | 3 | 11 | 145 | 2 | ✓ | all | 5 | rational |
| 3.11.258809 | 3 | 11 | 145 | 2 | ✓ | all | 5 | rational |
| 3.11.258810 | 3 | 11 | 146 | 2 | ✓ | all | 5 | rational |
| 3.11.258811 | 3 | 11 | 145 | 2 | ✓ | all | 5 | rational |
| 3.11.258812 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.258820 | 3 | 11 | 145 | 1 | ✓ | all | 5 | rational |
| 3.11.258834 | 3 | 11 | 144 | 1 | ✓ | all | 5 | rational |
| 3.11.258849 | 3 | 11 | 143 | 8 | ✓ | all | 5 | rational |
| 3.11.258911 | 3 | 11 | 146 | 2 | ✓ | all | 5 | rational |