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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 22,451–22,500
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.11.186086 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.186089 | 3 | 11 | 148 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.186094 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.186095 | 3 | 11 | 150 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.186096 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.186097 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.186099 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.186107 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.186108 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.186109 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.186111 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.186112 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.186115 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.186116 | 3 | 11 | 147 | 1 | ✓ | all | 1 | rational |
| 3.11.186117 | 3 | 11 | 147 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.186119 | 3 | 11 | 150 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.186120 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.186121 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.186122 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.186125 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.186126 | 3 | 11 | 148 | 1 | ✓ | all | 1 | empty |
| 3.11.186131 | 3 | 11 | 149 | 2 | ✓ | all | 1 | rational |
| 3.11.186132 | 3 | 11 | 151 | 1 | ✓ | all | 1 | rational |
| 3.11.186133 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.186135 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.186136 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.186250 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.186251 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.186253 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.186254 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.186255 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.186289 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.186292 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.186293 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.186294 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.186327 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.186328 | 3 | 11 | 148 | 1 | ✓ | all | 1 | empty |
| 3.11.186329 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.186330 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.186332 | 3 | 11 | 148 | 1 | ✓ | all but 2 | 1 | rational over Q(a)/(a^2 - a + 1) |
| 3.11.186333 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.186344 | 3 | 11 | 147 | 1 | ✓ | all | 1 | empty |
| 3.11.186345 | 3 | 11 | 147 | 1 | ✓ | all | 1 | empty |
| 3.11.186346 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.186349 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.186350 | 3 | 11 | 147 | 2 | ✓ | all | 1 | rational |
| 3.11.186351 | 3 | 11 | 148 | 2 | ✓ | all | 1 | rational |
| 3.11.186359 | 3 | 11 | 147 | 1 | ✓ | all | 1 | rational |
| 3.11.186360 | 3 | 11 | 147 | 2 | ✓ | all | 1 | rational |
| 3.11.186361 | 3 | 11 | 147 | 1 | ✓ | all | 1 | rational |