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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.
5,849,183 matroids, showing 22,101–22,150
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.11.184296 | 3 | 11 | 147 | 1 | ✓ | all | 1 | rational |
| 3.11.184298 | 3 | 11 | 146 | 2 | ✓ | all | 1 | empty |
| 3.11.184300 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.184301 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.184303 | 3 | 11 | 147 | 1 | ✓ | all | 1 | rational |
| 3.11.184304 | 3 | 11 | 149 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.184305 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.184307 | 3 | 11 | 148 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.184309 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.184313 | 3 | 11 | 147 | 1 | ✓ | all but 3 | 1 | rational |
| 3.11.184318 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.184319 | 3 | 11 | 149 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.184321 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational over Q(a)/(a^2 + 1) |
| 3.11.184323 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.184324 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.184326 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.184327 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.184329 | 3 | 11 | 149 | 1 | ✓ | all | 1 | empty |
| 3.11.184330 | 3 | 11 | 148 | 1 | ✓ | all | 1 | empty |
| 3.11.184331 | 3 | 11 | 148 | 1 | ✓ | all | 1 | empty |
| 3.11.184333 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.184337 | 3 | 11 | 147 | 1 | ✓ | all | 1 | empty |
| 3.11.184342 | 3 | 11 | 146 | 2 | ✓ | all | 1 | rational over Q(a)/(a^2 - a - 1) |
| 3.11.184343 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.184346 | 3 | 11 | 147 | 1 | ✓ | all | 1 | point over Q(a)/(a^2 + 1) |
| 3.11.184349 | 3 | 11 | 146 | 2 | ✓ | all | 1 | empty |
| 3.11.184351 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.184352 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.184353 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.184355 | 3 | 11 | 148 | 1 | ✓ | all but 2 | 1 | empty |
| 3.11.184359 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.184361 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.184362 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.184364 | 3 | 11 | 151 | 1 | ✓ | all | 1 | rational |
| 3.11.184370 | 3 | 11 | 149 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.184373 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.184375 | 3 | 11 | 150 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.184404 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.184405 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.184407 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.184409 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.184410 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.184416 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.184417 | 3 | 11 | 148 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.184420 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.184421 | 3 | 11 | 147 | 1 | ✓ | all | 1 | rational |
| 3.11.184423 | 3 | 11 | 148 | 1 | ✓ | all | 1 | empty |
| 3.11.184424 | 3 | 11 | 148 | 1 | ✓ | all but 2,5 | 1 | rational |
| 3.11.184425 | 3 | 11 | 150 | 1 | ✓ | all but 2,3 | 1 | rational |
| 3.11.184434 | 3 | 11 | 148 | 1 | ✓ | all but 2 | 1 | rational |