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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.
381,906 matroids, showing 19,401–19,450
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.12.373396 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.373413 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.373577 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.373579 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.373583 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.373629 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.373642 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.373651 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.373680 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.373700 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.373815 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.373847 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.373872 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.373977 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.373981 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.374022 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.374028 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.374045 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.374078 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.374091 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.374097 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.374114 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.374149 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.374152 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.374153 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.374161 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.374189 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.374211 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.374232 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.374239 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.374247 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.374274 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.374286 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.374289 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.374291 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.374292 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.374353 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.374356 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.374371 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.374389 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.374392 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.374401 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.374515 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.374516 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.374518 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.374527 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.374557 | 3 | 12 | 209 | 2 | ✓ | all | 6 | ? |
| 3.12.374563 | 3 | 12 | 211 | 4 | ✓ | all | 6 | ? |
| 3.12.374582 | 3 | 12 | 210 | 1 | ✓ | all | 6 | ? |
| 3.12.374583 | 3 | 12 | 210 | 1 | ✓ | all | 6 | ? |