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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 22,051–22,100
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.11.183972 | 3 | 11 | 149 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.183976 | 3 | 11 | 150 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.183979 | 3 | 11 | 149 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.183980 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.183982 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.183983 | 3 | 11 | 148 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.183988 | 3 | 11 | 151 | 1 | ✓ | all | 1 | rational |
| 3.11.183990 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.183992 | 3 | 11 | 150 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.184118 | 3 | 11 | 148 | 1 | ✓ | all but 2 | 1 | rational over Q(a)/(a^2 - a + 1) |
| 3.11.184120 | 3 | 11 | 147 | 1 | ✓ | all | 1 | rational |
| 3.11.184122 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.184123 | 3 | 11 | 149 | 1 | ✓ | all but 2,3 | 1 | rational |
| 3.11.184145 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.184147 | 3 | 11 | 147 | 1 | ✓ | all | 1 | empty |
| 3.11.184148 | 3 | 11 | 147 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.184179 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.184187 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.184234 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.184235 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.184237 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.184238 | 3 | 11 | 147 | 1 | ✓ | all | 1 | rational |
| 3.11.184239 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.184241 | 3 | 11 | 148 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.184242 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.184244 | 3 | 11 | 149 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.184245 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.184246 | 3 | 11 | 148 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.184253 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.184254 | 3 | 11 | 147 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.184256 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.184257 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational over Q(a)/(a^3 - a^2 + 1) |
| 3.11.184259 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.184260 | 3 | 11 | 148 | 1 | ✓ | all but 2 | 1 | rational over Q(a)/(a^2 + 1) |
| 3.11.184261 | 3 | 11 | 148 | 1 | ✓ | all but 2,3 | 1 | rational |
| 3.11.184271 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.184272 | 3 | 11 | 147 | 1 | ✓ | all | 1 | rational |
| 3.11.184273 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.184275 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.184276 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.184278 | 3 | 11 | 147 | 1 | ✓ | all | 1 | rational |
| 3.11.184279 | 3 | 11 | 146 | 1 | ✓ | all | 1 | rational |
| 3.11.184281 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.184282 | 3 | 11 | 149 | 1 | ✓ | all but 3 | 1 | rational |
| 3.11.184283 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.184285 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.184290 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.184291 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.184293 | 3 | 11 | 148 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.184295 | 3 | 11 | 147 | 1 | ✓ | all | 1 | rational |