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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 18,751–18,800
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.12.124266 | 3 | 12 | 208 | 1 | ✓ | all | 0 | ? |
| 3.12.124277 | 3 | 12 | 211 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.124287 | 3 | 12 | 210 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.124296 | 3 | 12 | 210 | 1 | ✓ | all | 0 | ? |
| 3.12.124306 | 3 | 12 | 210 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.124330 | 3 | 12 | 210 | 1 | ✓ | all | 0 | ? |
| 3.12.124345 | 3 | 12 | 209 | 1 | ✓ | all | 0 | ? |
| 3.12.124346 | 3 | 12 | 210 | 1 | ✓ | all but 3 | 0 | ? |
| 3.12.124355 | 3 | 12 | 209 | 1 | ✓ | all but 3 | 0 | ? |
| 3.12.124374 | 3 | 12 | 210 | 1 | ✓ | all | 0 | ? |
| 3.12.124409 | 3 | 12 | 210 | 1 | ✓ | all but 5 | 0 | ? |
| 3.12.124410 | 3 | 12 | 209 | 1 | ✓ | all | 0 | ? |
| 3.12.124411 | 3 | 12 | 209 | 1 | ✓ | all but 3 | 0 | ? |
| 3.12.124414 | 3 | 12 | 210 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.124422 | 3 | 12 | 209 | 1 | ✓ | all but 3 | 0 | ? |
| 3.12.124480 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.124509 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.124531 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.124542 | 3 | 12 | 208 | 1 | ✓ | all | 0 | ? |
| 3.12.124547 | 3 | 12 | 210 | 1 | ✓ | all | 0 | ? |
| 3.12.124548 | 3 | 12 | 210 | 1 | ✓ | all | 0 | ? |
| 3.12.124572 | 3 | 12 | 209 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.124588 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.124601 | 3 | 12 | 209 | 1 | ✓ | all but 3 | 0 | ? |
| 3.12.124605 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.124630 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.124662 | 3 | 12 | 209 | 1 | ✓ | all but 2,7 | 0 | ? |
| 3.12.124665 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.124686 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.124707 | 3 | 12 | 209 | 1 | ✓ | all | 0 | ? |
| 3.12.124729 | 3 | 12 | 209 | 1 | ✓ | all but 2,11 | 0 | ? |
| 3.12.124730 | 3 | 12 | 209 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.124737 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.124768 | 3 | 12 | 211 | 1 | ✓ | all but 2,3,11 | 0 | ? |
| 3.12.124786 | 3 | 12 | 210 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.124877 | 3 | 12 | 211 | 2 | ✓ | all but 2 | 0 | ? |
| 3.12.124886 | 3 | 12 | 210 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.124890 | 3 | 12 | 211 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.124918 | 3 | 12 | 209 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.124921 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.124933 | 3 | 12 | 208 | 1 | ✓ | all | 0 | ? |
| 3.12.124950 | 3 | 12 | 210 | 1 | ✓ | all but 2,3,7 | 0 | ? |
| 3.12.124990 | 3 | 12 | 208 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.124997 | 3 | 12 | 210 | 1 | ✓ | all | 0 | ? |
| 3.12.125007 | 3 | 12 | 210 | 1 | ✓ | all | 0 | ? |
| 3.12.125037 | 3 | 12 | 210 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.125048 | 3 | 12 | 208 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.125052 | 3 | 12 | 210 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.125055 | 3 | 12 | 210 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.125061 | 3 | 12 | 210 | 1 | ✓ | all but 2 | 0 | ? |