Search
…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 21,651–21,700
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.11.181238 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.181239 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.181241 | 3 | 11 | 147 | 1 | ✓ | all | 1 | point over Q(a)/(a^3 - a^2 + 1) |
| 3.11.181242 | 3 | 11 | 147 | 1 | ✓ | all | 1 | point over Q(a)/(a^2 - 2) |
| 3.11.181243 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.181245 | 3 | 11 | 147 | 1 | ✓ | all | 1 | rational |
| 3.11.181246 | 3 | 11 | 147 | 1 | ✓ | all | 1 | rational |
| 3.11.181248 | 3 | 11 | 152 | 2 | ✓ | all but 2,3 | 1 | rational |
| 3.11.181249 | 3 | 11 | 151 | 2 | ✓ | all but 2 | 1 | rational |
| 3.11.181250 | 3 | 11 | 151 | 2 | ✓ | all but 2 | 1 | rational |
| 3.11.181257 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.181258 | 3 | 11 | 150 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.181259 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.181261 | 3 | 11 | 151 | 1 | ✓ | all | 1 | rational |
| 3.11.181262 | 3 | 11 | 150 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.181264 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.181265 | 3 | 11 | 150 | 1 | ✓ | all but 2,3 | 1 | rational |
| 3.11.181266 | 3 | 11 | 151 | 2 | ✓ | all | 1 | rational |
| 3.11.181275 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.181276 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.181277 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.181279 | 3 | 11 | 149 | 1 | ✓ | all but 2,3 | 1 | rational |
| 3.11.181280 | 3 | 11 | 149 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.181281 | 3 | 11 | 149 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.181283 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.181284 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.181286 | 3 | 11 | 150 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.181287 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.181288 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.181290 | 3 | 11 | 150 | 2 | ✓ | all | 1 | rational |
| 3.11.181295 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.181296 | 3 | 11 | 149 | 1 | ✓ | all but 2,3 | 1 | rational |
| 3.11.181298 | 3 | 11 | 151 | 4 | ✓ | all | 1 | rational |
| 3.11.181299 | 3 | 11 | 150 | 2 | ✓ | all | 1 | rational |
| 3.11.181301 | 3 | 11 | 150 | 4 | ✓ | all | 1 | rational |
| 3.11.181302 | 3 | 11 | 151 | 2 | ✓ | all | 1 | rational |
| 3.11.181304 | 3 | 11 | 150 | 2 | ✓ | all but 2,3 | 1 | rational |
| 3.11.181305 | 3 | 11 | 148 | 2 | ✓ | all | 1 | rational |
| 3.11.181307 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.181308 | 3 | 11 | 149 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.181309 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.181312 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.181316 | 3 | 11 | 150 | 1 | ✓ | all but 3 | 1 | rational |
| 3.11.181345 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.181346 | 3 | 11 | 149 | 2 | ✓ | all | 1 | rational |
| 3.11.181348 | 3 | 11 | 150 | 2 | ✓ | all | 1 | rational |
| 3.11.181349 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.181352 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.181353 | 3 | 11 | 149 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.181359 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |