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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 19,251–19,300
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.12.131503 | 3 | 12 | 208 | 1 | ✓ | all | 0 | ? |
| 3.12.131510 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.131511 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,7 | 0 | ? |
| 3.12.131518 | 3 | 12 | 210 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.131526 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5,7 | 0 | ? |
| 3.12.131532 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.131537 | 3 | 12 | 209 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.131551 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.131585 | 3 | 12 | 209 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.131592 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.131627 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.131648 | 3 | 12 | 209 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.131666 | 3 | 12 | 208 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.131669 | 3 | 12 | 210 | 1 | ✓ | all but 2,3,7 | 0 | ? |
| 3.12.131690 | 3 | 12 | 210 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.131709 | 3 | 12 | 210 | 1 | ✓ | all but 2,3,7 | 0 | ? |
| 3.12.131710 | 3 | 12 | 209 | 1 | ✓ | all but 3 | 0 | ? |
| 3.12.131713 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5,7 | 0 | ? |
| 3.12.131726 | 3 | 12 | 209 | 1 | ✓ | all but 2,11 | 0 | ? |
| 3.12.131752 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,5,7,11 | 0 | ? |
| 3.12.131780 | 3 | 12 | 210 | 1 | ✓ | all but 3 | 0 | ? |
| 3.12.131783 | 3 | 12 | 209 | 1 | ✓ | all | 0 | ? |
| 3.12.131829 | 3 | 12 | 209 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.131834 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5,7 | 0 | ? |
| 3.12.131844 | 3 | 12 | 208 | 1 | ✓ | all but 2,7,11 | 0 | ? |
| 3.12.131874 | 3 | 12 | 207 | 1 | ✓ | all but 2,3,7 | 0 | ? |
| 3.12.131875 | 3 | 12 | 208 | 1 | ✓ | all | 0 | ? |
| 3.12.131882 | 3 | 12 | 209 | 1 | ✓ | all | 0 | ? |
| 3.12.131922 | 3 | 12 | 212 | 2 | ✓ | all but 2,3,5,7 | 0 | ? |
| 3.12.131929 | 3 | 12 | 211 | 2 | ✓ | all | 0 | ? |
| 3.12.131996 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5,7,11 | 0 | ? |
| 3.12.132038 | 3 | 12 | 210 | 1 | ✓ | all | 0 | ? |
| 3.12.132086 | 3 | 12 | 209 | 1 | ✓ | all | 0 | ? |
| 3.12.132109 | 3 | 12 | 209 | 1 | ✓ | all but 2,7 | 0 | ? |
| 3.12.132118 | 3 | 12 | 208 | 1 | ✓ | all | 0 | ? |
| 3.12.132122 | 3 | 12 | 209 | 1 | ✓ | all | 0 | ? |
| 3.12.132128 | 3 | 12 | 208 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.132152 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.132163 | 3 | 12 | 208 | 1 | ✓ | all | 0 | ? |
| 3.12.132195 | 3 | 12 | 209 | 1 | ✓ | all | 0 | ? |
| 3.12.132196 | 3 | 12 | 209 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.132201 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.132225 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,5,7,11 | 0 | ? |
| 3.12.132261 | 3 | 12 | 209 | 1 | ✓ | all but 2,7 | 0 | ? |
| 3.12.132275 | 3 | 12 | 208 | 1 | ✓ | all but 3 | 0 | ? |
| 3.12.132383 | 3 | 12 | 209 | 1 | ✓ | all but 5 | 0 | ? |
| 3.12.132418 | 3 | 12 | 210 | 1 | ✓ | all but 3 | 0 | ? |
| 3.12.132430 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.132465 | 3 | 12 | 209 | 1 | ✓ | all | 0 | ? |
| 3.12.132519 | 3 | 12 | 208 | 1 | ✓ | all but 2 | 0 | ? |