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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.
381,906 matroids, showing 18,351–18,400
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.12.346008 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.346049 | 3 | 12 | 210 | 1 | ✓ | all | 6 | ? |
| 3.12.346051 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.346055 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.346109 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.346130 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.346154 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.346168 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.346170 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.346261 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.346285 | 3 | 12 | 208 | 2 | ✓ | all | 6 | ? |
| 3.12.346287 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.346294 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.346298 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.346310 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.346330 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.346331 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.346357 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.346376 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.346378 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.346380 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.346384 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.346399 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.346408 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.346412 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.346428 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.346437 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.346456 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.346460 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.346494 | 3 | 12 | 206 | 1 | ✓ | all | 6 | ? |
| 3.12.346509 | 3 | 12 | 207 | 2 | ✓ | all | 6 | ? |
| 3.12.346513 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.346528 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.346551 | 3 | 12 | 206 | 1 | ✓ | all | 6 | ? |
| 3.12.346553 | 3 | 12 | 212 | 4 | ✓ | all | 6 | ? |
| 3.12.346585 | 3 | 12 | 210 | 2 | ✓ | all | 6 | ? |
| 3.12.346588 | 3 | 12 | 210 | 2 | ✓ | all | 6 | ? |
| 3.12.346612 | 3 | 12 | 210 | 1 | ✓ | all | 6 | ? |
| 3.12.346640 | 3 | 12 | 210 | 1 | ✓ | all | 6 | ? |
| 3.12.346641 | 3 | 12 | 210 | 1 | ✓ | all | 6 | ? |
| 3.12.346651 | 3 | 12 | 210 | 1 | ✓ | all | 6 | ? |
| 3.12.346655 | 3 | 12 | 210 | 1 | ✓ | all | 6 | ? |
| 3.12.346665 | 3 | 12 | 211 | 1 | ✓ | all | 6 | ? |
| 3.12.346667 | 3 | 12 | 210 | 1 | ✓ | all | 6 | ? |
| 3.12.346687 | 3 | 12 | 211 | 1 | ✓ | all | 6 | ? |
| 3.12.346701 | 3 | 12 | 210 | 1 | ✓ | all | 6 | ? |
| 3.12.346703 | 3 | 12 | 210 | 1 | ✓ | all | 6 | ? |
| 3.12.346712 | 3 | 12 | 210 | 1 | ✓ | all | 6 | ? |
| 3.12.346733 | 3 | 12 | 210 | 1 | ✓ | all | 6 | ? |
| 3.12.346790 | 3 | 12 | 210 | 1 | ✓ | all | 6 | ? |