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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 19,051–19,100
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.12.128601 | 3 | 12 | 210 | 1 | ✓ | all | 0 | ? |
| 3.12.128607 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,11 | 0 | ? |
| 3.12.128644 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,11 | 0 | ? |
| 3.12.128647 | 3 | 12 | 209 | 1 | ✓ | all | 0 | ? |
| 3.12.128664 | 3 | 12 | 209 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.128708 | 3 | 12 | 210 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.128725 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5,13 | 0 | ? |
| 3.12.128734 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,7 | 0 | ? |
| 3.12.128761 | 3 | 12 | 210 | 1 | ✓ | all but 2,3,7 | 0 | ? |
| 3.12.128765 | 3 | 12 | 208 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.128786 | 3 | 12 | 210 | 1 | ✓ | all but 2,3,7 | 0 | ? |
| 3.12.128800 | 3 | 12 | 209 | 1 | ✓ | all | 0 | ? |
| 3.12.128829 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,7 | 0 | ? |
| 3.12.128845 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,7 | 0 | ? |
| 3.12.128871 | 3 | 12 | 208 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.128890 | 3 | 12 | 210 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.128902 | 3 | 12 | 210 | 1 | ✓ | all but 2,3,7 | 0 | ? |
| 3.12.128923 | 3 | 12 | 210 | 1 | ✓ | all but 2,3,7 | 0 | ? |
| 3.12.128946 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.128948 | 3 | 12 | 210 | 1 | ✓ | all but 3 | 0 | ? |
| 3.12.128955 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,7 | 0 | ? |
| 3.12.128991 | 3 | 12 | 209 | 1 | ✓ | all but 2,7 | 0 | ? |
| 3.12.129005 | 3 | 12 | 210 | 1 | ✓ | all | 0 | ? |
| 3.12.129010 | 3 | 12 | 210 | 2 | ✓ | all but 2,3 | 0 | ? |
| 3.12.129014 | 3 | 12 | 212 | 1 | ✓ | all but 2,3,7 | 0 | ? |
| 3.12.129031 | 3 | 12 | 211 | 1 | ✓ | all but 2,3,7 | 0 | ? |
| 3.12.129094 | 3 | 12 | 209 | 1 | ✓ | all | 0 | ? |
| 3.12.129099 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,7 | 0 | ? |
| 3.12.129113 | 3 | 12 | 210 | 1 | ✓ | all but 5 | 0 | ? |
| 3.12.129138 | 3 | 12 | 209 | 1 | ✓ | all but 5 | 0 | ? |
| 3.12.129185 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.129187 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5,7,11 | 0 | ? |
| 3.12.129188 | 3 | 12 | 209 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.129206 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,7 | 0 | ? |
| 3.12.129209 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,7 | 0 | ? |
| 3.12.129210 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,7 | 0 | ? |
| 3.12.129221 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.129228 | 3 | 12 | 209 | 1 | ✓ | all but 2,11 | 0 | ? |
| 3.12.129229 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,7 | 0 | ? |
| 3.12.129319 | 3 | 12 | 210 | 1 | ✓ | all but 3 | 0 | ? |
| 3.12.129357 | 3 | 12 | 209 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.129411 | 3 | 12 | 208 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.129412 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,7 | 0 | ? |
| 3.12.129423 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,7 | 0 | ? |
| 3.12.129440 | 3 | 12 | 209 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.129447 | 3 | 12 | 209 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.129462 | 3 | 12 | 210 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.129469 | 3 | 12 | 209 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.129474 | 3 | 12 | 209 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.129487 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,5 | 0 | ? |