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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 19,351–19,400
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.12.133973 | 3 | 12 | 210 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.133980 | 3 | 12 | 211 | 1 | ✓ | all but 2,3,5,7 | 0 | ? |
| 3.12.133982 | 3 | 12 | 211 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.133998 | 3 | 12 | 211 | 1 | ✓ | all but 2,7 | 0 | ? |
| 3.12.134008 | 3 | 12 | 210 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.134056 | 3 | 12 | 210 | 1 | ✓ | all | 0 | ? |
| 3.12.134089 | 3 | 12 | 211 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.134117 | 3 | 12 | 209 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.134145 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,7 | 0 | ? |
| 3.12.134154 | 3 | 12 | 209 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.134170 | 3 | 12 | 210 | 1 | ✓ | all but 2,3,7 | 0 | ? |
| 3.12.134186 | 3 | 12 | 210 | 1 | ✓ | all but 2,3,7 | 0 | ? |
| 3.12.134210 | 3 | 12 | 210 | 1 | ✓ | all but 2,3,7 | 0 | ? |
| 3.12.134239 | 3 | 12 | 210 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.134299 | 3 | 12 | 209 | 1 | ✓ | all but 2,5,13 | 0 | ? |
| 3.12.134300 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.134324 | 3 | 12 | 210 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.134345 | 3 | 12 | 208 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.134375 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,7 | 0 | ? |
| 3.12.134402 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.134404 | 3 | 12 | 210 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.134474 | 3 | 12 | 210 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.134495 | 3 | 12 | 210 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.134515 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.134522 | 3 | 12 | 210 | 1 | ✓ | all but 2,3,5,7 | 0 | ? |
| 3.12.134556 | 3 | 12 | 210 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.134575 | 3 | 12 | 209 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.134581 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.134583 | 3 | 12 | 209 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.134611 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,7 | 0 | ? |
| 3.12.134618 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.134632 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.134642 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5,7,11,13,19 | 0 | ? |
| 3.12.134661 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.134662 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,5,13 | 0 | ? |
| 3.12.134667 | 3 | 12 | 210 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.134670 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.134684 | 3 | 12 | 210 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.134695 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,7 | 0 | ? |
| 3.12.134697 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.134702 | 3 | 12 | 209 | 1 | ✓ | all but 2,7 | 0 | ? |
| 3.12.134729 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,7,11 | 0 | ? |
| 3.12.134742 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5,7,11 | 0 | ? |
| 3.12.134754 | 3 | 12 | 210 | 1 | ✓ | all but 2,3,7,11 | 0 | ? |
| 3.12.134764 | 3 | 12 | 210 | 1 | ✓ | all but 2,11 | 0 | ? |
| 3.12.134768 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5,7,11 | 0 | ? |
| 3.12.134773 | 3 | 12 | 209 | 1 | ✓ | all but 2,7 | 0 | ? |
| 3.12.134792 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.134799 | 3 | 12 | 210 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.134805 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5 | 0 | ? |