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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.
2,030,492 matroids, showing 21,951–22,000
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.12.169160 | 3 | 12 | 208 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.169166 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,5,7 | 0 | ? |
| 3.12.169169 | 3 | 12 | 208 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.169198 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,5,7 | 0 | ? |
| 3.12.169211 | 3 | 12 | 208 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.169213 | 3 | 12 | 208 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.169240 | 3 | 12 | 208 | 1 | ✓ | all | 0 | ? |
| 3.12.169246 | 3 | 12 | 208 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.169249 | 3 | 12 | 208 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.169294 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5,7 | 0 | ? |
| 3.12.169305 | 3 | 12 | 209 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.169350 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,5,7 | 0 | ? |
| 3.12.169370 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5,7 | 0 | ? |
| 3.12.169382 | 3 | 12 | 211 | 1 | ✓ | all but 2,3,7 | 0 | ? |
| 3.12.169390 | 3 | 12 | 210 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.169441 | 3 | 12 | 210 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.169471 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.169530 | 3 | 12 | 210 | 1 | ✓ | all but 2,3,5,7,11 | 0 | ? |
| 3.12.169600 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.169611 | 3 | 12 | 210 | 1 | ✓ | all but 3 | 0 | ? |
| 3.12.169614 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.169627 | 3 | 12 | 209 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.169628 | 3 | 12 | 208 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.169631 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.169643 | 3 | 12 | 210 | 1 | ✓ | all but 2,3,5,7 | 0 | ? |
| 3.12.169679 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.169691 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.169703 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.169707 | 3 | 12 | 210 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.169709 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5,7 | 0 | ? |
| 3.12.169710 | 3 | 12 | 209 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.169740 | 3 | 12 | 210 | 1 | ✓ | all | 0 | ? |
| 3.12.169742 | 3 | 12 | 210 | 1 | ✓ | all | 0 | ? |
| 3.12.169743 | 3 | 12 | 210 | 1 | ✓ | all but 2,3,5,7,11 | 0 | ? |
| 3.12.169771 | 3 | 12 | 209 | 1 | ✓ | all but 3 | 0 | ? |
| 3.12.169775 | 3 | 12 | 210 | 1 | ✓ | all | 0 | ? |
| 3.12.169778 | 3 | 12 | 210 | 1 | ✓ | all but 2,11 | 0 | ? |
| 3.12.169779 | 3 | 12 | 210 | 1 | ✓ | all but 3 | 0 | ? |
| 3.12.169808 | 3 | 12 | 209 | 1 | ✓ | all | 0 | ? |
| 3.12.169819 | 3 | 12 | 208 | 1 | ✓ | all | 0 | ? |
| 3.12.169826 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.169832 | 3 | 12 | 209 | 1 | ✓ | all but 3 | 0 | ? |
| 3.12.169840 | 3 | 12 | 209 | 1 | ✓ | all | 0 | ? |
| 3.12.169843 | 3 | 12 | 208 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.169860 | 3 | 12 | 209 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.169863 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,7 | 0 | ? |
| 3.12.169868 | 3 | 12 | 209 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.169873 | 3 | 12 | 209 | 1 | ✓ | all | 0 | ? |
| 3.12.169882 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,5,7,11 | 0 | ? |
| 3.12.169883 | 3 | 12 | 208 | 1 | ✓ | all but 2,5 | 0 | ? |