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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 19,501–19,550
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.12.136004 | 3 | 12 | 210 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.136007 | 3 | 12 | 210 | 1 | ✓ | all but 3 | 0 | ? |
| 3.12.136038 | 3 | 12 | 209 | 1 | ✓ | all | 0 | ? |
| 3.12.136073 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,5,7,11 | 0 | ? |
| 3.12.136081 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.136095 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,7 | 0 | ? |
| 3.12.136106 | 3 | 12 | 208 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.136134 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.136139 | 3 | 12 | 209 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.136156 | 3 | 12 | 208 | 1 | ✓ | all but 2,7 | 0 | ? |
| 3.12.136157 | 3 | 12 | 210 | 1 | ✓ | all | 0 | ? |
| 3.12.136159 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.136160 | 3 | 12 | 209 | 1 | ✓ | all | 0 | ? |
| 3.12.136170 | 3 | 12 | 209 | 1 | ✓ | all | 0 | ? |
| 3.12.136179 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,5,7 | 0 | ? |
| 3.12.136187 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.136191 | 3 | 12 | 210 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.136192 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.136194 | 3 | 12 | 209 | 1 | ✓ | all | 0 | ? |
| 3.12.136233 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,5,7,11,17 | 0 | ? |
| 3.12.136247 | 3 | 12 | 208 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.136252 | 3 | 12 | 208 | 1 | ✓ | all | 0 | ? |
| 3.12.136256 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.136270 | 3 | 12 | 209 | 1 | ✓ | all but 2,7 | 0 | ? |
| 3.12.136279 | 3 | 12 | 209 | 1 | ✓ | all but 2,7 | 0 | ? |
| 3.12.136297 | 3 | 12 | 210 | 1 | ✓ | all but 2,3,5,7 | 0 | ? |
| 3.12.136325 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,7 | 0 | ? |
| 3.12.136331 | 3 | 12 | 210 | 1 | ✓ | all but 2,3,5,17 | 0 | ? |
| 3.12.136347 | 3 | 12 | 209 | 1 | ✓ | all | 0 | ? |
| 3.12.136362 | 3 | 12 | 208 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.136387 | 3 | 12 | 208 | 1 | ✓ | all but 2,11 | 0 | ? |
| 3.12.136391 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.136396 | 3 | 12 | 209 | 1 | ✓ | all but 5 | 0 | ? |
| 3.12.136399 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5,7,11,13 | 0 | ? |
| 3.12.136413 | 3 | 12 | 208 | 1 | ✓ | all but 2,7 | 0 | ? |
| 3.12.136414 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,7 | 0 | ? |
| 3.12.136415 | 3 | 12 | 208 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.136442 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.136450 | 3 | 12 | 209 | 1 | ✓ | all but 2,23 | 0 | ? |
| 3.12.136458 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.136464 | 3 | 12 | 208 | 1 | ✓ | all | 0 | ? |
| 3.12.136486 | 3 | 12 | 210 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.136522 | 3 | 12 | 208 | 1 | ✓ | all | 0 | ? |
| 3.12.136578 | 3 | 12 | 210 | 1 | ✓ | all but 2,3,5,13 | 0 | ? |
| 3.12.136584 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.136591 | 3 | 12 | 209 | 1 | ✓ | all | 0 | ? |
| 3.12.136593 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.136610 | 3 | 12 | 208 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.136675 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,5,7,17 | 0 | ? |
| 3.12.136681 | 3 | 12 | 210 | 1 | ✓ | all but 2 | 0 | ? |