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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.
5,849,183 matroids, showing 22,301–22,350
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.11.185511 | 3 | 11 | 150 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.185512 | 3 | 11 | 150 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.185513 | 3 | 11 | 151 | 1 | ✓ | all | 1 | rational |
| 3.11.185515 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.185516 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.185517 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.185525 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.185526 | 3 | 11 | 150 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.185528 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.185530 | 3 | 11 | 149 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.185531 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.185532 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.185534 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.185535 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.185536 | 3 | 11 | 150 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.185571 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.185572 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.185573 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.185575 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.185576 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.185577 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.185579 | 3 | 11 | 149 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.185580 | 3 | 11 | 149 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.185595 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.185596 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.185597 | 3 | 11 | 149 | 2 | ✓ | all | 1 | rational |
| 3.11.185600 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.185601 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.185603 | 3 | 11 | 150 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.185605 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.185607 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.185609 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.185610 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.185611 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.185616 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.185620 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.185626 | 3 | 11 | 147 | 1 | ✓ | all | 1 | rational |
| 3.11.185627 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.185628 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.185630 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.185631 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.185634 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.185635 | 3 | 11 | 148 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.185636 | 3 | 11 | 147 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.185638 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.185639 | 3 | 11 | 149 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.185640 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.185641 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.185644 | 3 | 11 | 148 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.185649 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |